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

TL;DR

This paper derives traveling-wave solutions for the Korteweg-de Vries-Burgers equations using factorizations of the reduced ODEs, revealing new details and correcting previous solutions.

Contribution

It introduces a factorization method to find solutions of the KdV-Burgers equations, including solutions of Bernoulli and Riccati types, and corrects and extends prior results.

Findings

All previously reported solutions are recovered.

Some solutions are corrected and new details are revealed.

The method provides a systematic way to derive solutions.

Abstract

Travelling-wave solutions of the standard and compound form of Korteweg-de Vries-Burgers equations are found using factorizations of the corresponding reduced ordinary differential equations. The procedure leads to solutions of Bernoulli equations of nonlinearity 3/2 and 2 (Riccati), respectively. Introducing 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 interesting details of these solitary waves that have been overlooked before this investigation