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

High frequency perturbation of cnoidal waves in KdV