Transverse nonlinear instability for two-dimensional dispersive models
classification
🧮 math.AP
keywords
nonlinearinstabilitysolitarytransversedispersivemodelsprovewaves
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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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