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Instabilities in the two-dimensional cubic nonlinear Schrodinger equation

John D. Carter·Harvey Segur
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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.

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John D. Carter, Harvey Segur. 2003-02-17. Instabilities in the two-dimensional cubic nonlinear Schrodinger equation. https://doi.org/10.1103/physreve.68.045601

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