Nonexistence of soliton-like solutions for defocusing generalized KdV equations
Abstract
In this short note, we consider the global dynamics of the defocusing generalized KdV equations: ut + uxxx = (|u|p-1u)x. We use Tao's theorem that the energy moves faster than mass to prove a moment type dispersion estimate. As an application of the dispersion estimate, we show that there is no soliton-like solutions with decaying assumption.
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