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Jun 29, 2018
06/18

by
Nikolai A. Kudryashov; Dmitry I. Sinelshchikov

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We study the perturbed Burgers-Korteweg-de Vries equation. This equation can be used for the description of nonlinear waves in a liquid with gas bubbles and for the description of nonlinear waves on a fluid layer flowing down an inclined plane. We investigate the integrability of this equation using the Painlev\'{e} approach. We show that the perturbed Burgers-Korteweg-de Vries equation does not belong to the class of integrable equations. Classical and nonclassical symmetries admitted by this...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1608.00833

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0.0

Jun 30, 2018
06/18

by
F. Fontanela; A. Grolet; L. Salles; A. Chabchoub; N. Hoffmann

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In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex nonlinear phenomena can be expected. We consider a cyclically symmetric system of coupled weakly nonlinear undamped oscillators that could be considered a minimal model for different cyclic and symmetric aerospace structures experiencing large deformations. The...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1704.00695

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0.0

Jun 29, 2018
06/18

by
Roy H. Goodman

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The nonlinear Schr\"odinger/Gross-Pitaevskii (NLS/GP) equation is considered in the presence of three equally-spaced potentials. The problem is reduced to a finite-dimensional Hamiltonian system by a Galerkin truncation. Families of oscillatory orbits are sought in the neighborhoods of the system's nine branches of standing wave solutions. Normal forms are computed in the neighborhood of these branches' various Hamiltonian Hopf and saddle-node bifurcations, showing how the oscillatory...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1612.02041

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1.0

Jun 29, 2018
06/18

by
Armin Kekić; Robert A. Van Gorder

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We study solitary wave propagation in 1D granular crystals with Hertz-like interaction potentials. We consider interfaces between media with different exponents in the interaction potential. For an interface with increasing interaction potential exponent along the propagation direction we obtain mainly transmission with delayed secondary transmitted and reflected pulses. For interfaces with decreasing interaction potential exponent we observe both significant reflection and transmission of the...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1612.07617

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0.0

Jun 30, 2018
06/18

by
G. Gambino; M. C. Lombardo; M. Sammartino

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In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel--Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show how nonlinear diffusion intensifies the tendency to pattern formation; %favors the mechanism of pattern formation with respect to the classical linear diffusion case; in particular, unlike the case of classical linear diffusion, the Turing instability can occur...

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1403.0351

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0.0

Jun 29, 2018
06/18

by
Takahiro Kohsokabe; Kunihiko Kaneko

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Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by diffusion from the fixed boundary. We introduced a spatial map, whose temporal sequence, under selection criteria from multiple stationary solutions, can completely reproduce the emergent pattern, by replacing the time with space. The relationship of the pattern...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1603.01038

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0.0

Jun 30, 2018
06/18

by
Yannis Kominis

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Soliton propagation dynamics under the presence of a complex potential are investigated. A large variety of qualitatively different potentials, including periodic, semi-infinite periodic and localized potentials, is considered. Cases of both symmetric and non-symmetric potentials are studied in terms of their effect on soliton dynamics. The rich set of dynamical features of soliton propagation include dynamical trapping, periodic and non-periodic soliton mass variation and non-reciprocal...

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1408.5335

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0.0

Jun 30, 2018
06/18

by
Stavros Komineas; Stephen P. Shipman; Stephanos Venakides

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Photons and excitons in a semiconductor microcavity interact to form exciton-polariton condensates. These are governed by a nonlinear quantum-mechanical system involving exciton and photon wavefunctions. We calculate all non-traveling harmonic soliton solutions for the one-dimensional lossless system. There are two frequency bands of bright solitons when the inter-exciton interactions produce an attractive nonlinearity and two frequency bands of dark solitons when the nonlinearity is repulsive....

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1409.4067

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1.0

Jun 30, 2018
06/18

by
Paulino Monroy Castillero; Arik Yochelis

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A generic distinct mechanism for the emergence of spatially localized states embedded in an oscillatory background is demonstrated by using 2:1 frequency locking oscillatory system. The localization is of Turing type and appears in two space dimensions as a comb-like state in either $\pi$ phase shifted Hopf oscillations or inside a spiral core. Specifically, the localized states appear in absence of the well known flip-flop dynamics (associated with collapsed homoclinic snaking) that is known...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1702.08556

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Jun 30, 2018
06/18

by
Rodislav Driben; Yaroslav V. Kartashov; Boris A. Malomed; Torsten Meier; Lluis Torner

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We show, by means of numerical and analytical methods, that media with a repulsive nonlinearity which grows from the center to the periphery support a remarkable variety of previously unknown complex stationary and dynamical three-dimensional solitary-wave states. Peanut-shaped modulation profiles give rise to vertically symmetric and antisymmetric vortex states, and novel stationary hybrid states, built of top and bottom vortices with opposite topological charges, as well as robust dynamical...

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1405.5977

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Jun 29, 2018
06/18

by
Christopher D. Marcotte; Roman O. Grigoriev

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This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1605.00115

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Jun 29, 2018
06/18

by
M. Banerjee; V. Vougalter; V. Volpert

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The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms corresponds to the nonlocal consumption of resources while another one describes reproduction with different phenotypes. Linear stability analysis of the homogeneous in space stationary solution is carried out. Existence of travelling waves is proved in the case of narrow kernels of the integrals. Periodic travelling waves are...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1601.04257

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0.0

Jun 30, 2018
06/18

by
Bing-Wei Li; Mei-Chun Cai; Hong Zhang; Alexander V. Panfilov; Hans Dierckx

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Chirality is one of the most fundamental properties of many physical, chemical and biological systems. However, the mechanisms underlying the onset and control of chiral symmetry are largely understudied. We investigate possibility of chirality control in a chemical excitable system (the BZ reaction) by application of a chiral (rotating) electric field using the Oregonator model. We find that unlike previous findings, we can achieve the chirality control not only in the field rotation...

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1403.1116

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0.0

Jun 27, 2018
06/18

by
J. Javaloyes; T. Ackemann; A. Hurtado

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Motionless domains walls representing heteroclinic temporal or spatial orbits typically exist only for very specific parameters. This report introduces a novel mechanism for stabilizing temporal domain walls away from the Maxwell point opening up new possibilities to encode information in dynamical systems. It is based on anti-periodic regimes in a delayed system close to a bistable situation, leading to a cancellation of the average drift velocity. The results are demonstrated in a normal form...

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1503.02830

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1.0

Jun 29, 2018
06/18

by
Russell Campbell; Gian-Luca Oppo

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A model of a Bose-Einstein condensate in a ring optical lattice with atomic dissipations applied at a stationary or at a moving location on the ring is presented. The localized dissipation is shown to generate and stabilize both stationary and traveling lattice solitons. Among many localized solutions, we have generated spatially stationary quasiperiodic lattice soltions and a family of traveling lattice solitons with two intensity peaks per potential well with no counterpart in the discrete...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1606.06773

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0.0

Jun 29, 2018
06/18

by
S. P. Wallen; J. Lee; D. Mei; C. Chong; P. G. Kevrekidis; N. Boechler

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We report on the existence of discrete breathers in a one-dimensional, mass-in-mass chain with linear intersite coupling and nonlinear Hertzian local resonators, which is motivated by recent studies of the dynamics of microspheres adhered to elastic substrates. After predicting theoretically the existence of the discrete breathers in the continuum and anticontinuum limits of intersite coupling, we use numerical continuation to compute a family of breathers interpolating between the two regimes...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1605.03377

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0.0

Jun 29, 2018
06/18

by
V. N. Biktashev; M. A. Tsyganov

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Solitons, defined as nonlinear waves which can reflect from boundaries or transmit through each other, are found in conservative, fully integrable systems. Similar phenomena, dubbed quasi-solitons, have been observed also in dissipative, "excitable" systems, either at finely tuned parameters (near a bifurcation) or in systems with cross-diffusion. Here we demonstrate that quasi-solitons can be robustly observed in excitable systems with excitable kinetics and with self-diffusion only....

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1605.00521

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0.0

Jun 29, 2018
06/18

by
Avinash Khare; Fred Cooper; Avadh Saxena

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We consider the coupled nonlinear Dirac equations (NLDE's) in 1+1 dimensions with scalar-scalar self interactions $\frac{ g_1^2}{2} ( {\bpsi} \psi)^2 + \frac{ g_2^2}{2} ( {\bphi} \phi)^2 + g_3^2 ({\bpsi} \psi) ( {\bphi} \phi)$ as well as vector-vector interactions of the form $\frac{g_1^2 }{2} (\bpsi \gamma_{\mu} \psi)(\bpsi \gamma^{\mu} \psi)+ \frac{g_2^2 }{2} (\bphi \gamma_{\mu} \phi)(\bphi \gamma^{\mu} \phi) + g_3^2 (\bpsi \gamma_{\mu} \psi)(\bphi \gamma^{\mu} \phi ). $ Writing the two...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1603.08043

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0.0

Jun 30, 2018
06/18

by
Steffen Martens; Christopher Ryll; Jakob Löber; Fredi Tröltzsch; Harald Engel

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The ability to control a desired dynamics or pattern in reaction-diffusion systems has attracted considerable attention over the last decades and it is still a fundamental problem in applied nonlinear science. Besides traveling waves, moving localized spots -- also called dissipative solitons -- represent yet another important class of self-organized spatio-temporal structures in non-equilibrium dissipative systems. In this work, we focus attention to control aspects and present an efficient...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.04246

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0.0

Jun 29, 2018
06/18

by
Felix Tabbert; Christian Schelte; Mustapha Tlidi; Svetlana Gurevich

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We report on the dynamics of localized structures in an inhomogeneous Swift-Hohenberg model describing pattern formation in the transverse plane of an optical cavity. This real order parameter equation is valid close to the second order critical point associated with bistability. The optical cavity is illuminated by an inhomogeneous spatial gaussian pumping beam, and subjected to time-delayed feedback. The gaussian injection beam breaks the translational symmetry of the system by exerting an...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1611.10256

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0.0

Jun 30, 2018
06/18

by
Nikolay A. Kudryashov; Dmitry I. Sinelshchikov

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The perturbed Korteweg--de Vries equation is considered. This equation is used for the description of one--dimensional viscous gas dynamics, nonlinear waves in a liquid with gas bubbles and nonlinear acoustic waves. The integrability of this equation is investigated using the Painlev\'e approach. The condition for parameters for the integrability of the perturbed Korteweg--de Vries equation equation is established. New classical and nonclassical symmetries admitted by this equation are found....

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1409.6703

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3.0

Jun 29, 2018
06/18

by
J. Nathan Kutz; Joshua L. Proctor; Steven L. Brunton

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We consider the application of Koopman theory to nonlinear partial differential equations. We demonstrate that the observables chosen for constructing the Koopman operator are critical for enabling an accurate approximation to the nonlinear dynamics. If such observables can be found, then the dynamic mode decomposition algorithm can be enacted to compute a finite-dimensional approximation of the Koopman operator, including its eigenfunctions, eigenvalues and Koopman modes. Judiciously chosen...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1607.07076

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1.0

Jun 30, 2018
06/18

by
Julien Siebert; Sergio Alonso; Markus Bär; Eckehard Schöll

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A one-component bistable reaction-diffusion system with asymmetric nonlocal coup ling is derived as limiting case of a two-component activator-inhibitor reaction -diffusion model with differential advection. The effects of asymmetric nonlocal couplings in such a bistable reaction-diffusi on system are then compared to the previously studied case of a system with symm etric nonlocal coupling. We carry out a linear stability analysis of the spatially homogeneous steady sta tes of the model and...

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1401.3111

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1.0

Jun 30, 2018
06/18

by
Frederike Kneer; Klaus Obermayer; Markus A. Dahlem

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The effect of advection on the critical minimal speed of traveling waves is studied. Previous theoretical studies estimated the effect on the velocity of stable fast waves and predicted the existence of a critical advection strength below which propagating waves are not supported anymore. In this paper, the critical advection strength is calculated taking into account the unstable slow wave solution. Thereby, theoretical results predict, that advection can induce stable wave propagation in the...

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1404.5824

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1.0

Jun 30, 2018
06/18

by
J. Cuevas-Maraver; P. G. Kevrekidis; A. B. Aceves; A. Saxena

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In the present work, we explore a nonlinear Dirac equation motivated as the continuum limit of a binary waveguide array model. We approach the problem both from a near-continuum perspective as well as from a highly discrete one. Starting from the former, we see that the continuum Dirac solitons can be continued for all values of the discretization (coupling) parameter, down to the uncoupled (so-called anti-continuum) limit where they result in a 9-site configuration. We also consider...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.00679

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1.0

Jun 28, 2018
06/18

by
J. Cuevas-Maraver; P. G. Kevrekidis; A. Saxena; A. Comech; R. Lan

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We explore a prototypical two-dimensional model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral stability analysis, illustrating the potential of spinor solutions consisting of a soliton in one component and a vortex in the other to be neutrally stable in a wide parametric interval of frequencies. Solutions of higher vorticity are generically unstable and split into lower charge...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1512.03973

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2.0

Jun 29, 2018
06/18

by
Alexey Samokhin

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Superposition of explicit (analytic) monotone non-increasing shock waves for the KdV-Burgers equation is studied, modelled numerically and graphically presented. Initial profile chosen as a sum of two such shock waves gradually transforms into a single shock wave of a somewhat complex yet predictable structure. This transformation is demonstrated in detail.

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1604.00505

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9.0

Jun 25, 2018
06/18

by
Y. N. Truong Vu; J. D'Ambroise; P. G. Kevrekidis; F. Kh. Abdullaev

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In the present paper we consider an optical system with a $\chi^{(2)}$-type nonlinearity and unspecified $\mathcal{PT}$-symmetric potential functions. Considering this as an inverse problem and positing a family of exact solutions in terms of cnoidal functions, we solve for the resulting potential functions in a way that ensures the potentials obey the requirements of $\mathcal{PT}$-symmetry. We then focus on case examples of soliton and periodic solutions for which we present a stability...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1501.00519

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1.0

Jun 30, 2018
06/18

by
Branislav N. Aleksić; Najdan B. Aleksić; Milan S. Petrović; Aleksandra I. Strinić; Milivoj R. Belić

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We apply the variational approach to solitons in highly nonlocal nonlinear media in $D=1,2,3$ dimensions. We compare results obtained by the variational approach with those obtained in the accessible soliton approximation, by considering the same system of equations in the same spatial region and under the same boundary conditions. To assess the accuracy of these approximations, we also compare them with the numerical solution of the equations. We discover that the variational highly nonlocal...

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1410.2580

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1.0

Jun 30, 2018
06/18

by
Y. Shen; P. G. Kevrekidis; S. Sen; A. Hoffman

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Our aim in the present work is to develop approximations for the collisional dynamics of traveling waves in the context of granular chains in the presence of precompression. To that effect, we aim to quantify approximations of the relevant Hertzian FPU-type lattice through both the Korteweg-de Vries (KdV) equation and the Toda lattice. Using the availability in such settings of both 1-soliton and 2-soliton solutions in explicit analytical form, we initialize such coherent structures in the...

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1405.1768

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3.0

Jun 29, 2018
06/18

by
Michelle D. Maiden; Mark. A. Hoefer

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In this work, modulation of periodic interfacial waves on a conduit of viscous liquid is explored utilizing Whitham theory and Nonlinear Schr\"odinger (NLS) theory. Large amplitude periodic wave modulation theory does not require integrability of the underlying model equation, yet in practice, either integrable equations are studied or the full extent of Whitham (wave-averaging) theory is not developed. The governing conduit equation is nonlocal with nonlinear dispersion and is not...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1607.00460

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1.0

Jun 30, 2018
06/18

by
Jennie D'Ambroise; Panayotis G. Kevrekidis; Boris A. Malomed

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We introduce a ladder-shaped chain with each rung carrying a $\mathcal{PT}$ -symmetric gain-loss dipole. The polarity of the dipoles is staggered along the chain, meaning that a rung bearing gain-loss is followed by one bearing loss-gain. This renders the system $\mathcal{PT}$-symmetric in both horizontal and vertical directions. The system is governed by a pair of linearly coupled discrete nonlinear Schr\"{o}dinger (DNLS) equations with self-focusing or defocusing cubic onsite...

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1409.7413

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1.0

Jun 28, 2018
06/18

by
Haitao Xu; Panayotis G. Kevrekidis; Dmitry E. Pelinovsky

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Vortices symmetric with respect to simultaneous parity and time reversing transformations are considered on the square lattice in the framework of the discrete nonlinear Schr\"{o}dinger equation. The existence and stability of vortex configurations is analyzed in the limit of weak coupling between the lattice sites, when predictions on the elementary cell of a square lattice (i.e., a single square) can be extended to a large (yet finite) array of lattice cells. Our analytical predictions...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1511.01878

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4.0

Jun 27, 2018
06/18

by
Danial Saadatmand; Sergey V. Dmitriev; Panayotis G. Kevrekidis

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Solitons are very effective in transporting energy over great distances and collisions between them can produce high energy density spots of relevance to phase transformations, energy localization and defect formation among others. It is then important to study how energy density accumulation scales in multi-soliton collisions. In this study, we demonstrate that the maximal energy density that can be achieved in collision of $N$ slowly moving kinks and antikinks in the integrable sine-Gordon...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1506.01389

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1.0

Jun 29, 2018
06/18

by
Pavel P. Kizin

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The work is devoted to numerical investigation of stability of stationary localized modes ("gap solitons") for the one-dimentional nonlinear Schr\"odinger equation (NLSE) with periodic potential and repulsive nonlinearity. Two classes of the modes are considered: a bound state of a pair of in-phase and out-of-phase fundamental gap solitons (FGSs) from the first bandgap separated by various number of empty potential wells. Using the standard framework of linear stability analysis,...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1611.09262

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3.0

Jun 26, 2018
06/18

by
L. D. Bookman; M. A. Hoefer

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Droplet solitons are a strongly nonlinear, inherently dynamic structure in the magnetization of ferromagnets, balancing dispersion (exchange energy) with focusing nonlinearity (strong perpendicular anisotropy). Large droplet solitons have the approximate form of a circular domain wall sustained by precession and, in contrast to single magnetic vortices, are predicted to propagate in an extended, homogeneous magnetic medium. In this work, multiscale perturbation theory is utilized to develop an...

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1501.05276

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1.0

Jun 30, 2018
06/18

by
Will Cousins; Themistoklis P. Sapsis

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We study the evolution of localized wave groups in unidirectional water wave envelope equations (nonlinear Schrodinger (NLS) and modified NLS (MNLS)). These localizations of energy can lead to disastrous extreme responses (rogue waves). Previous studies have focused on the role of energy distribution in the frequency domain in the formation of extreme waves. We analytically quantify the role of spatial localization, introducing a novel technique to reduce the underlying PDE dynamics to a simple...

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1411.4175

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1.0

Jun 28, 2018
06/18

by
C. Chong; E. Kim; E. G. Charalampidis; H. Kim; F. Li; P. G. Kevrekidis; J. Lydon; C. Daraio; J. Yang

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This article explores the excitation of different vibrational states in a spatially extended dynamical system through theory and experiment. As a prototypical example, we consider a one-dimensional packing of spherical particles (a so-called granular chain) that is subject to harmonic boundary excitation. The combination of the multi-modal nature of the system and the strong coupling between the particles due to the nonlinear Hertzian contact force leads to broad regions in frequency where...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1510.04753

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1.0

Jun 29, 2018
06/18

by
Arash Azhand; Rico Buchholz; Jan F. Totz; H. Engel

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While free scroll rings are non-stationary objects that either grow or contract with time, spatial confinement can have a large impact on their evolution reaching from significant lifetime extension [J. F. Totz , H. Engel, and O. Steinbock, New J. Phys. 17, 093043 (2015)] up to formation of stable stationary and breathing pacemakers [A. Azhand, J. F. Totz, and H. Engel, Europhys. Lett. 108, 10004 (2014)]. Here, we explore the parameter range in which the interaction between an axis-symmetric...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1601.00848

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1.0

Jun 29, 2018
06/18

by
F. Baronio; S. Wabnitz; Y. Kodama

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There is considerable fundamental and applicative interest in obtaining non-diffractive and non-dispersive spatio-temporal localized wave packets propagating in optical cubic nonlinear or Kerr media. Here, we analytically predict the existence of a novel family of spatio-temporal dark lump solitary wave solutions of the (2+1)D nonlinear Schr\"odinger equation. Dark lumps represent multi-dimensional holes of light on a continuous wave background. We analytically derive the dark lumps from...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1602.08464

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2.0

Jun 30, 2018
06/18

by
H. Xu; P. G. Kevrekidis; A. Stefanov

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In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as Mass-in-Mass systems. We use 3 distinct approaches to identify relevant traveling waves. The first consists of a direct solution of the traveling wave problem. The second one consists of the solution of the Fourier tranformed variant of the problem. or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) of the problem in real space....

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1412.5462

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1.0

Jun 29, 2018
06/18

by
R. I. Woodward; E. J. R. Kelleher

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We reveal the existence of slowly-decaying dark solitons in the radiation build-up dynamics of bright pulses in all-normal dispersion mode-locked fiber lasers, numerically modeled in the framework of a generalized nonlinear Schr\"odinger equation. The evolution of noise perturbations to quasi-stationary dark solitons is examined, and the significance of background shape and soliton-soliton collisions on the eventual soliton decay is established. We demonstrate the role of a restoring force...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1601.03330

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Jun 30, 2018
06/18

by
S. Karthiga; V. K. Chandrasekar; M. Senthilvelan; M. Lakshmanan

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We investigate the dynamics of a coupled waveguide system with competing linear and nonlinear loss-gain profiles which can facilitate power saturation. We show the usefulness of the model in achieving unidirectional beam propagation. In this regard, the considered type of coupled waveguide system has two drawbacks, (i) difficulty in achieving perfect isolation of light in a waveguide and (ii) existence of blow-up type behavior for certain input power situations. We here show a nonlinear...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.02752

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Jun 30, 2018
06/18

by
Li-Chen Zhao; Liming Ling; Jian-wen Qi; Zhan-Ying Yang; Wen-Li Yang

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We study rogue wave excitation pattern in a two-component Bose-Einstein condensate with pair-transition effects. The results indicate that rogue wave excitation can exist on a stripe phase background for which there are cosine and sine wave background in the two components respectively. The rogue wave peak can be much lower than the ones of scalar matter wave rogue waves, and varies with the wave period changing. Both rogue wave pattern and rogue wave number on temporal-spatial plane are much...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1702.07130

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Jun 30, 2018
06/18

by
Abhik Mukherjee; Anirban Bose; M. S. Janaki

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Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from...

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1405.4107

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Jun 30, 2018
06/18

by
S. E. Kurushina; E. A. Shapovalova

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We present a study of disorder origination and growth inside an ordered phase processes induced by the presence of multiplicative noise within mean-field approximation. Our research is based on the study of solutions of the nonlinear self-consistent Fokker-Planck equation for a stochastic spatially extended model of a chemical reaction. We carried out numerical simulation of the probability distribution density dynamics and statistical characteristics of the system under study for varying noise...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.04480

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Jun 29, 2018
06/18

by
Fernando V. Barbosa; André L. A. Penna; Rogelma M. S. Ferreira; Keila L. Novais; Jefferson A. R. da Cunha; Fernando A. Oliveira

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In this work, we study the pattern solutions of doubly nonlocal logistic map that include spatial kernels in both growth and competition terms. We show that this map includes as a particular case the nonlocal Fisher-Kolmogorov equation, and we demonstrate the existence of three kinds of stationary nonlinear solutions: one uniform, one cosine type that we refer to as wavelike solution, and another in the form of Gaussian. We also obtain analytical expressions that describe the nonlinear pattern...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1601.07148

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Jun 30, 2018
06/18

by
E. G. Charalampidis; P. G. Kevrekidis; D. J. Frantzeskakis; B. A. Malomed

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We study a two-component nonlinear Schr{\"{o}}dinger system with equal, repulsive cubic interactions and different dispersion coefficients in the two components. We consider states that have a dark solitary wave in one component. Treating it as a frozen one, we explore the possibility of the formation of bright-solitonic structures in the other component. We identify bifurcation points at which such states emerge in the bright component in the linear limit and explore their continuation...

Topics: Nonlinear Sciences, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1407.1335

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Jun 28, 2018
06/18

by
Jianke Yang

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A normal form is derived for Hamiltonian-Hopf bifurcations of solitary waves in generalized nonlinear Schr\"odinger equations. This normal form is a simple second-order nonlinear ordinary differential equation that is asymptotically accurate in describing solution dynamics near Hamiltonian-Hopf bifurcations. When the nonlinear coefficient in this normal form is complex, which occurs if the second harmonic of the Hopf bifurcation frequency falls inside the continuous spectrum of the system,...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1510.00949

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Jun 30, 2018
06/18

by
Artem Cherenkov; Valery Lobanov; Michael Gorodetsky

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We present the results of asymptotic and numerical analysis of dissipative Kerr solitons in whispering gallery mode microresonators influenced by higher order dispersive terms leading to the appearance of a dispersive wave (Cherenkov radiation). Combining direct perturbation method with the method of moments we find expressions for the frequency, strength, spectral width of the dispersive wave and soliton velocity. Mutual influence of the soliton and dispersive wave was studied. The formation...

Topics: Pattern Formation and Solitons, Nonlinear Sciences

Source: http://arxiv.org/abs/1702.08750