Asymptotic behaviour of solutions to the Korteweg-de Vries-Burgers equation (Q1979108)

The paper is devoted to asymptotic behaviour of solutions to the KdVB equation with initial data, which have different limits \(c_{\pm }\) at \(\pm \infty ,\) where \(c_{+}<c_{-}.\) Power decay of a perturbation to the monotone travelling wave solution to the KdVB equation for \(t\rightarrow \infty \) is proved.