Transverse nonlinear instability for two-dimensional dispersive models

Details Transverse nonlinear instability for two-dimensional dispersive models Transverse nonlinear instability for two-dimensional dispersive models

2006-12-18

arxiv.org/abs/math/0612494v3

Mathematics

Analysis of PDEs

26 pages, minor changes

Scientific paper

We present a method to prove nonlinear instability of solitary waves in
dispersive models. Two examples are analyzed: we prove the nonlinear long time
instability of the KdV solitary wave (with respect to periodic transverse
perturbations) under a KP-I flow and the transverse nonlinear instability of
solitary waves for the cubic nonlinear Schr\"odinger equation.

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