Soliton Solutions for Some Nonlinear Partial Differential Equations in Mathematical Physics Using He’s Variational Method

Mohammed K. Elboree 1
  • 1 Mathematics Department, Faculty of Science, South Valley University, Qena, Egypt
Mohammed K. Elboree

Abstract

In this paper, we constructed the variational principles for Bogoyavlensky–Konopelchenko equation, the generalized (3+1)-dimensional nonlinear wave in liquid containing gas bubbles and a new coupled Kadomtsev–Petviashvili (KP) equation via He’s semi-inverse method. Based on this formulation, we obtained the solitary wave solutions via Ritz method. We explained the properties of the soliton waves numerically by some figures. Finally, the physical interpretation for these solutions are obtained.

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The International Journal of Nonlinear Sciences and Numerical Simulation publishes original papers on all subjects relevant to nonlinear sciences and numerical simulation. The journal is directed at researchers in nonlinear sciences, engineers, and computational scientists, economists, and others, who either study the nature of nonlinear problems or conduct numerical simulations of nonlinear problems.

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