Eur. Phys. J. Plus (2016) 131: 385
https://doi.org/10.1140/epjp/i2016-16385-x

Regular Article

Painlevé analysis, integrability and exact solutions for a (2 + 1)-dimensional generalized Nizhnik-Novikov-Veselov equation

¹ Department of Information Management, College of Management, Shanghai University, 200444, Shanghai, China
² Department of Mathematics, East China University of Science and Technology, 200237, Shanghai, China

^* e-mail: xugq@staff.shu.edu.cn

Received: 16 July 2016
Accepted: 8 October 2016
Published online: 7 November 2016

Abstract

Under investigation in this paper is a (2 + 1)-dimensional generalized NNV equation, which includes as many important nonlinear models as its particular cases. First, we perform the Painlevé test for the generalized NNV equation with the help of symbolic computation, and it is shown that this generalized equation admits the Painlevé property for one set of parametric choices. For the newly obtained integrable equation, we then employ the binary Bell polynomial method to construct the bilinear form, N-soliton solution, bilinear Bäcklund transformation and Lax pair in a systematic way. In addition, some new doubly periodic wave solutions with two arbitrary functions are obtained by means of truncated Painlevé expansions. Finally, the collisions of multiple solitons and periodic waves are interesting and shown by some graphs.