Large data scattering for the defocusing supercritical generalized KdV equation
Abstract
We consider the defocusing supercritical generalized Korteweg-de Vries (gKdV) equation ∂t u+∂x3u-∂x(uk+1)=0, where k>4 is an even integer number. We show that if the initial data u0 belongs to H1 then the corresponding solution is global and scatters in H1. Our method of proof is inspired on the compactness method introduced by C. Kenig and F. Merle.
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