Second term of asymptotics for KdVB equation with large initial data

Abstract

We consider the Cauchy problem for the Korteweg-de Vries-Burgers\nequation. Global existence and smoothing effect for the Cauchy problem to\nthe Korteweg-de Vries-Burgers equation\nwas proved previously for the case\nof large initial data. Recently the first term of the large time\nasymptotics was obtained without restriction on the size of the initial\ndata. The aim of the present paper is to obtain the second term of the\nlarge time asymptotic behavior of solutions to the Cauchy problem for the\nKorteweg-de Vries-Burgers equation\nin the case of the initial data of arbitrary size.