Type: Article

A simplified approach to obtaining a sharp asymptotics to the modified Korteweg-de Vries equation for large time

Hayashi, Nakao; Naumkin, Pavel I.;

Abstract:

We study the global in time existence of small solutions and a sharp time decay estimate to the Cauchy problem for the modified Korteweg–de Vries equation. We consider the real-valued initial data. Also we assume that the mean value of the initial data vanishes. We present a simple proof comparing with the previous works which is based on the development of the Factorization Techniques and a new function space of solutions. Our function space yields a sharp time decay of solutions in the uniform norm.