American Institute of Mathematical Sciences

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

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

Anwar Ja'afar Mohamad Jawad 1, , Mohammad Mirzazadeh 2, and  Anjan Biswas 3,

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.
Keywords: traveling waves, tanh-coth method, Gardner-KP equation., $G^{\prime}/G$-expansion.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
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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show all references

References:
[1]

Communications in Nonlinear Science and Numerical Simulation, 14 (2009), 734-748. doi: 10.1016/j.cnsns.2007.12.004.  Google Scholar

[2]

Romanian Journal of Physics, 58 (2013), 729-748.  Google Scholar

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Advanced Studies in Theoretical Physics, 2 (2008), 787-794.  Google Scholar

[4]

Applied Mathematics and Computation, 214 (2009), 645-647. doi: 10.1016/j.amc.2009.04.001.  Google Scholar

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Applied Mathematics and Computation, 217 (2010), 1771-1773. doi: 10.1016/j.amc.2009.09.042.  Google Scholar

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Journal of Applied Fluid Mechanics, 7 (2014), 603-609. Google Scholar

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Romaninan Reports in Physics, 65 (2013), 27-62. Google Scholar

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Journal of Modern Optics, 60 (2013), 1627-1636. doi: 10.1080/09500340.2013.850777.  Google Scholar

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European Physical Journal, Plus, 128 (2013), p140. Google Scholar

[10]

Nonlinear Dynamics, 66 (2011), 497-507. doi: 10.1007/s11071-010-9928-7.  Google Scholar

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Journal of Applied Fluid Mechanics, 6 (2013), 339-350. Google Scholar

[12]

Journal of Applied Fluid Mechanics, 7 (2014), 711-718. Google Scholar

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World Applied Science Journal, 13 (2011), 662-666. Google Scholar

[19]

Communications in Nonlinear Science and Numerical Simulations, 17 (2012), 1493-1499. doi: 10.1016/j.cnsns.2011.09.023.  Google Scholar

[20]

Applied Mathematical Modelling, 35 (2011), 3991-3997. doi: 10.1016/j.apm.2011.02.001.  Google Scholar

[21]

Ain Shams Engineering Journal, 4 (2013), 493-499. doi: 10.1016/j.asej.2012.10.002.  Google Scholar

[22]

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[23]

Communications in Nonlinear Science and Numerical Simulations, 14 (2009), 1810-1815. doi: 10.1016/j.cnsns.2008.07.009.  Google Scholar

[24]

Applied Mathematics and Computation, 207 (2009), 279-282. doi: 10.1016/j.amc.2008.10.031.  Google Scholar

[25]

Canadian Journal of Physics, 89 (2011), 979-984. doi: 10.1139/p11-083.  Google Scholar

[26]

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Nonlinear Analysis: Modelling and Control, 17 (2012), 369-378.  Google Scholar

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International Journal of Computer Mathematics, 87 (2010), 1716-1725. doi: 10.1080/00207160802450166.  Google Scholar

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