SIMILARITY REDUCTIONS FOR A NONLINEAR WAVE EQUATION WITH DAMPING TERM

Abstract

Three types of similarity reductions are obtained for nonlinear wave equation with damping term utt-2buxxt+αuxxxx=β(unx)x(α>0,β≠0,n≥2)by the use of the direct reduction method due to Clarkson and Kruskal.It is shown that this equation is not integrable under the sense of Ablowitz's conjecture by analysing the Painlevé properties of these reduction equations.In addition,four families of exact solutions are found for this equation(n=2).