# American Institute of Mathematical Sciences

December  2015, 8(6): 1155-1164. doi: 10.3934/dcdss.2015.8.1155

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

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

Received  May 2015 Revised  August 2015 Published  December 2015

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.
Citation: Anwar Ja'afar Mohamad Jawad, Mohammad Mirzazadeh, Anjan Biswas. Dynamics of shallow water waves with Gardner-Kadomtsev-Petviashvili equation. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1155-1164. doi: 10.3934/dcdss.2015.8.1155
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