Regular Article

Painlevé analysis, group classification and exact solutions to the nonlinear wave equations

¹ School of Mathematical Sciences, Liaocheng University, Liaocheng, Shandong 252059, P.R. China
² School of Physics Science and Information Engineering, Liaocheng University, Liaocheng, Shandong 252059, P.R. China

^a e-mail: bzliuhanze@163.com

Received: 15 August 2019
Received in final form: 24 December 2019
Published online: 11 February 2020

Abstract

This paper is concerned with the general regular long-wave (RLW) types of equations. By the combination of Painlevé analysis and Lie group classification method, the conditional Painlevé property (PP) and Bäcklund transformations (BTs) of the nonlinear wave equations are provided under some conditions. Then, all of the point symmetries of the nonlinear RLW types of equations are obtained, the exact solutions to the equations are investigated. Particularly, some explicit solutions are provided by the special function and Φ-expansion method.