Eur. Phys. J. Plus (2016) 131: 390
https://doi.org/10.1140/epjp/i2016-16390-1

Regular Article

Periodic wave, breather wave and travelling wave solutions of a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation in fluids or plasmas

Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, 100191, Beijing, China

^* e-mail: gaoyt163@163.com

Received: 1 September 2016
Accepted: 18 October 2016
Published online: 8 November 2016

Abstract

In this paper, a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation is investigated, which has been presented as a model for the shallow water wave in fluids or the electrostatic wave potential in plasmas. By virtue of the binary Bell polynomials, the bilinear form of this equation is obtained. With the aid of the bilinear form, N -soliton solutions are obtained by the Hirota method, periodic wave solutions are constructed via the Riemann theta function, and breather wave solutions are obtained according to the extended homoclinic test approach. Travelling waves are constructed by the polynomial expansion method as well. Then, the relations between soliton solutions and periodic wave solutions are strictly established, which implies the asymptotic behaviors of the periodic waves under a limited procedure. Furthermore, we obtain some new solutions of this equation by the standard extended homoclinic test approach. Finally, we give a generalized form of this equation, and find that similar analytical solutions can be obtained from the generalized equation with arbitrary coefficients.