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
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.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2017