Instabilities in the two-dimensional cubic nonlinear Schrodinger equation
Abstract
The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional traveling wave solution of NLS with trivial phase is unstable with respect to some infinitesimal perturbation with two-dimensional structure. If the coefficients of the linear dispersion terms have the same sign then the only unstable perturbations have transverse wavelength longer than a well-defined cut-off. If the coefficients of the linear dispersion terms have opposite signs, then there is no such cut-off and as the wavelength decreases, the maximum growth rate approaches a well-defined limit.
Cite
@article{arxiv.nlin/0302041,
title = {Instabilities in the two-dimensional cubic nonlinear Schrodinger equation},
author = {John D. Carter and Harvey Segur},
journal= {arXiv preprint arXiv:nlin/0302041},
year = {2016}
}
Comments
4 pages, 4 figures