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arXiv · 1108.3363

Transverse stability of periodic traveling waves in Kadomtsev-Petviashvili equations: A numerical study

C. Klein·C. Sparber
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Abstract

We numerically investigate transverse stability and instability of so-called cnoidal waves, i.e., periodic traveling wave solutions of the Korteweg-de Vries equation, under the time-evolution of the Kadomtsev-Petviashvili equation. In particular, we find that in KP-I small amplitude cnoidal waves are stable (at least for spatially localized perturbations) and only become unstable above a certain threshold. In contrast to that, KP-II is found to be stable for all amplitudes, or, equivalently, wave speeds. This is in accordance with recent analytical results for solitary waves given in \cite{RT1, RT2}.

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C. Klein, C. Sparber. 2011-08-16. Transverse stability of periodic traveling waves in Kadomtsev-Petviashvili equations: A numerical study. https://arxiv.org/abs/1108.3363

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