Stability and instability of the KdV solitary wave under the KP-I flow

Details Stability and instability of the KdV solitary wave under the KP-I flow Stability and instability of the KdV solitary wave under the KP-I flow

2011-04-13

arxiv.org/abs/1104.2555v1

Mathematics

Analysis of PDEs

Scientific paper

We consider the KP-I and gKP-I equations in $\mathbb{R}\times (\mathbb{R}/2\pi \mathbb{Z})$. We prove that the KdV soliton with subcritical speed $0c^*$, in the spirit of the work by Duyckaerts and Merle \cite{DM}, we sharpen our previous instability result and construct a global solution which is different from the solitary wave and its translates and which converges to the solitary wave as time goes to infinity. This last result also holds for the gKP-I equation.

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