Second term of asymptotics for KdVB equation with large initial data

Abstract

We consider the Cauchy problem for the Korteweg-de Vries-Burgers equation. Global existence and smoothing effect for the Cauchy problem to the Korteweg-de Vries-Burgers equation was proved previously for the case of large initial data. Recently the first term of the large time asymptotics was obtained without restriction on the size of the initial data. The aim of the present paper is to obtain the second term of the large time asymptotic behavior of solutions to the Cauchy problem for the Korteweg-de Vries-Burgers equation in the case of the initial data of arbitrary size.