Instabilities in the two-dimensional cubic nonlinear Schrodinger equation

Details Instabilities in the two-dimensional cubic nonlinear Schrodinger equation Instabilities in the two-dimensional cubic nonlinear Schrodinger equation

2003-02-17

arxiv.org/abs/nlin/0302041v1

Nonlinear Sciences

Pattern Formation and Solitons

4 pages, 4 figures

Scientific paper

10.1103/PhysRevE.68.045601

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.

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