New exact solutions for the variable coefficient modified KdV equation using direct reduction method

Abstract

In this paper, the direct reduction method combined with the homogeneous balance method is used to construct new exact solutions for the variable coefficient modified KdV model in fluid‐filled elastic tubes. The variable coefficient modified KdV is reduced to a Ricatti ordinary equation that has many exact solutions. The solutions obtained in this manuscript are new and recover other solutions obtained before in many literature. Copyright © 2012 John Wiley & Sons, Ltd.