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**1 - 4**of**4**### c ○ 2012 Society for Industrial and Applied Mathematics HIGH FREQUENCY PERTURBATION OF CNOIDAL WAVES IN

"... Abstract. The 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 a low frequency component (cnoidal wave) and high frequenc ..."

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Abstract. The 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 a low frequency component (cnoidal wave) and high frequency radiation is weak for finite time in the following sense: the radiation approximately satisfies the Airy equation. Key words. Korteweg–de Vries, KdV cnoidal waves, high frequency AMS subject classifications. 35Q53, 37K45 DOI. 10.1137/120868220

### HIGH FREQUENCY PERTURBATION OF CNOIDAL WAVES IN KDV

"... 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) ..."

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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.