Transverse nonlinear instability for two-dimensional dispersive models |
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| Authors: | F Rousset N Tzvetkov |
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| Institution: | 1. University of Nice-Sophia Antipolis, Laboratoire J.A. Dieudonné, 06108 Nice cedex 2, France;2. University of Lille 1, Laboratoire P. Painlevé, 59655 Villeneuve d''Ascq cedex, France |
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| Abstract: | 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 Schrödinger equation. |
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| Keywords: | Nonlinear instability Solitary waves Dispersive equations |
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