Travelling-wave solutions for Korteweg-de Vries-Burgers equations through factorizations

Abstract

"Travelling-wave solutions of the standard and compound form of Korteweg-de Vries-Burgers equations are found using factorizations of the correspond-ing reduced ordinary diferential equations. The procedure leads to solutions of Bernoulli equations of nonlinearity 3/2 and 2 (Riccati), respectively. In-troducing the initial conditions through an imaginary phase in the travelling coordinate, we obtain all the solutions previously reported, some of them being corrected here, and showing, at the same time, the presence of inter-esting details of these solitary waves that have been overlooked before this investigation."