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2.0

Jun 30, 2018
06/18

by
Yaron Hadad; Vladimir Zakharov

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This paper studies diagonal spacetime metrics. It is shown that the overdetermined Einstein vacuum equations are compatible if one Killing vector exists. The stability of plane gravitational waves of the Robinson type is studied. This stability problem bares a fantastic mathematical resemblance to the stability of the Schwarzschild black hole studied by Regge and Wheeler. Just like for the Schwarzschild black hole, the Robinson gravitational waves are proven to be stable with respect to small...

Topic: General Relativity and Quantum Cosmology

Source: http://arxiv.org/abs/1401.7251

3
3.0

Jun 29, 2018
06/18

by
Vladimir Zakharov; Donald Resio; Andrei Pushkarev

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The new ZRP wind input source term (Zakharov et al. 2012) is checked for its consistency via numerical simulation of Hasselmann equation. The results are compared to field experimental data, collected at different sites around the world, and theoretical predictions of self-similarity analysis. Good agreement is obtained for limited fetch and time domain statements

Topics: Atmospheric and Oceanic Physics, Physics

Source: http://arxiv.org/abs/1608.03790

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69

Sep 24, 2013
09/13

by
Dmitry Agafontsev; Vladimir Zakharov

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We measure evolution of spectra, spatial correlation functions and probability density functions (PDFs) of waves appearance for a set of one-dimensional NLS-like equations of focusing type, namely for the classical integrable Nonlinear Schrodinger equation (1), nonintegrable NLS equation accounting for dumping (linear dissipation, two- and three-photon absorption) and pumping terms (2) and generalized NLS equation accounting for six-wave interactions, dumping and pumping terms (3). All...

Source: http://arxiv.org/abs/1202.5763v4

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57

Sep 23, 2013
09/13

by
Vladimir Zakharov; Andrey Gelash

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We construct new exact solutions of the focusing Nonlinear Schr\"{o}dinger equation (NLSE). This is a soliton propagating on an unstable condensate. The Kuznetsov and Akhmediev solitons as well as the Peregrine instanton are particular cases of this new solution. We discuss applications of this new solution to the description of freak (rogue) waves in the ocean and in optical fibers.

Source: http://arxiv.org/abs/1109.0620v2

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8.0

Jun 27, 2018
06/18

by
Sergey A. Dyachenko; Dmitry Zakharov; Vladimir Zakharov

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We describe a broad class of bounded non-periodic potentials in one-dimensional stationary quantum mechanics having the same spectral properties as periodic potentials. The spectrum of the corresponding Schroedinger operator consists of a finite or infinite number of allowed bands separated by gaps. In this letter we consider the simplest class of potentials, whose spectra consist of an interval on the negative semiaxis and the entire positive axis. The potentials are reflectionless, and a...

Topics: Exactly Solvable and Integrable Systems, Mathematical Physics, Mathematics, Nonlinear Sciences

Source: http://arxiv.org/abs/1505.05806

3
3.0

Jun 29, 2018
06/18

by
Vladimir Zakharov

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The hypothesis on complete integrability of equations describing the potential motion of incompressible ideal fluid with free surface in 2-D space in presence and absence of gravity was formulated by Dyachenko and Zakharov in 1994 [1]. Later on, the same authors found that these equations have indefinite number of additional motion constants [2] that was an argument in support of the integrability hypothesis. In this article we formulate another argument in favor of this conjecture. It is known...

Topics: Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1604.04778