Eur. Phys. J. Plus (2017) 132: 29
https://doi.org/10.1140/epjp/i2017-11313-4

Regular Article

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

¹ Mathematics Department, Faculty of science, Taibah University, Al-Ula, Saudi Arabia
² Mathematics Department, Faculty of Science, Beni-Suef University, Beni Suef, Egypt

^* e-mail: Aly742001@yahoo.com

Received: 22 October 2016
Accepted: 21 December 2016
Published online: 23 January 2017

Abstract

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.