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Soliton solutions for (2+1) and (3+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony model equations and their applications

Tariq Kalim U. (School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, P.R. China + Department of Mathematics, Mirpur University of Science and Technology, Mirpur (AJK), Pakistan)
Seadawy Aly (Mathematics Department, Faculty of Science, Beni-Suef University, Egypt + Mathematics Department, Faculty of science, Taibah University, Al-Ula, Saudi Arabia)

The Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) model equations as a water wave model, are governing equations, for fluid flows, describes bidirectional propagating water wave surface. The soliton solutions for (2+1) and (3+1)-Dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equations have been extracted. The solitary wave ansatz method are adopted to approximate the solutions. The corresponding integrability criteria, also known as constraint conditions, naturally emerge from the analysis of the problem.

Keywords: solitary wave soliton, shock wave soliton, singular solitons, exact solutions