High frequency perturbation of cnoidal waves in KdV

Details High frequency perturbation of cnoidal waves in KdV High frequency perturbation of cnoidal waves in KdV

2011-03-21

arxiv.org/abs/1103.4135v1

Mathematics

Analysis of PDEs

23 pages

Scientific paper

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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