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Sep 23, 2013
09/13

by
Milan S. Petrovic; Aleksandra I. Strinic; Najdan B. Aleksic; Milivoj R. Belic

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We question physical existence of shape invariant solitons in three dimensional nematic liquid crystals. Using modified Petviashvili's method for finding eigenvalues and eigenfunctions, we determine shape invariant solitons in a realistic physical model that includes the highly nonlocal nature of the liquid crystal system. We check the stability of such solutions by propagating them for long distances. We establish that any noise added to the medium or to the fundamental solitons induces them...

Source: http://arxiv.org/abs/1110.5053v1

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Jun 29, 2018
06/18

by
Tai-Chia Lin; Milivoj R. Belic; Milan S. Petrovic; Hichem Hajaiej; Goong Chen

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The virial theorem is a nice property for the linear Schrodinger equation in atomic and molecular physics as it gives an elegant ratio between the kinetic and potential energies and is useful in assessing the quality of numerically computed eigenvalues. If the governing equation is a nonlinear Schrodinger equation with power-law nonlinearity, then a similar ratio can be obtained but there seems no way of getting any eigenvalue estimate. It is surprising as far as we are concerned that when the...

Topics: Nonlinear Sciences, Analysis of PDEs, Physics, Mathematics, Pattern Formation and Solitons, Optics,...

Source: http://arxiv.org/abs/1608.06102

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Jun 30, 2018
06/18

by
Yiqi Zhang; Xing Liu; Milivoj R. Belić; Weiping Zhong; Milan S. Petrović; Yanpeng Zhang

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We investigate the propagation of light beams including Hermite-Gauss, Bessel-Gauss and finite energy Airy beams in a linear medium with parabolic potential. Expectedly, the beams undergo oscillation during propagation, but quite unexpectedly they also perform automatic Fourier transform, that is, periodic change from the beam to its Fourier transform and back. The oscillating period of parity-asymmetric beams is twice that of the parity-symmetric beams. In addition to oscillation, the...

Topics: Physics, Optics

Source: http://arxiv.org/abs/1412.6648

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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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Jun 30, 2018
06/18

by
Yiqi Zhang; Milivoj R. Belić; Milan S. Petrović; Huaibin Zheng; Haixia Chen; Changbiao Li; Keqing Lu; Yanpeng Zhang

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We introduce two-dimensional (2D) linear and nonlinear Talbot effects. They are produced by propagating periodic 2D diffraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot effect originates from 2D rogue waves and forms in a bulk 3D nonlinear medium. The recurrences of an input rogue wave are observed at the Talbot length and at the half-Talbot length, with a \pi phase shift; no other recurrences are observed. Different from the nonlinear Talbot effect,...

Topics: Physics, Nonlinear Sciences, Optics, Pattern Formation and Solitons

Source: http://arxiv.org/abs/1412.0236