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arXiv · 1103.4135

High frequency perturbation of cnoidal waves in KdV

M. B. Erdoğan·N. Tzirakis·V. Zharnitsky
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Abstract

The Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. The interaction of a periodic solitary wave (cnoidal wave) with high frequency radiation of finite energy ($L^2$-norm) is studied. It is proved that the interaction of low frequency component (cnoidal wave) and high frequency radiation is weak for finite time in the following sense: the radiation approximately satisfies Airy equation.

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M. B. Erdoğan, N. Tzirakis, V. Zharnitsky. 2011-03-21. High frequency perturbation of cnoidal waves in KdV. https://arxiv.org/abs/1103.4135

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