Dynamics of shallow water waves with Gardner-Kadomtsev-Petviashvili equation

Anwar Ja'afar Mohamad  Jawad; Mohammad  Mirzazadeh; Anjan  Biswas

doi:10.3934/dcdss.2015.8.1155

Article Contents

2015, Volume 8, Issue 6: 1155-1164. Doi: 10.3934/dcdss.2015.8.1155

This issue Previous Article Dynamic systems based on preference graph and distance Next Article Periodic orbits for a generalized Friedmann-Robertson-Walker Hamiltonian system in dimension $6$

Dynamics of shallow water waves with Gardner-Kadomtsev-Petviashvili equation

1.
Computer Engineering Technique Department Al-Rafidain, University College, Baghdad
2.
Department of Engineering Sciences, Faculty of Technology and Engineering East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah
3.
Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277

Received: May 2015

Revised: August 2015

Published: December 2015

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Abstract

This paper obtains soliton and other solutions to the Gardner-Kadomtsev-Petviashvili equation that models shallow water wave equation in (1+2)-dimensions. There are three types of integration architectures that will be employed in order to obtain several forms of solution to this model. These are traveling wave hypothesis, improved $G^{\prime}/G$-expansion method and finally the tanh-coth hypothesis. The constraint conditions that are needed, for these solutions to exist, are also reported.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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