NONEXISTENCE OF SOLITON-LIKE SOLUTIONS FOR DEFOCUSING GENERALIZED KDV EQUATIONS

Abstract

We consider the global dynamics of the defocusing generalized KdV equation

partial derivative(t)u + partial derivative(3)(x)u = partial derivative(x)(vertical bar u vertical bar(P-1)u).

We use Tao's theorem [5] that the energy moves faster than the 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 a certain decaying assumption.