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Waves in Random and Complex Media Volume 21, 2011 - Issue 2
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Original Articles

Soliton solutions and conservation laws of the Gilson–Pickering equation

Ghodrat Ebadi Faculty of Mathematical Sciences, University of Tabriz, Tabriz 51666-14766, Iran
,
A.H. Kara School of Mathematics, University of the Witwatersrand, Johannesburg, Wits 2050, South Africa
,
Marko D. Petković Department of Mathematics and Computer Science, Faculty of Science and Mathematics, University of Niš, Višegradska 33, Niš 18000, Serbia
&
Anjan Biswas Applied Mathematics Research Center, Center for Research and Education in Optical Sciences and Applications, Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USACorrespondence[email protected]
Pages 378-385 | Received 18 Jan 2011, Accepted 28 Feb 2011, Published online: 28 Mar 2011
 
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Abstract

This paper obtains the soliton solutions of the Gilson–Pickering equation. The G′/G method will be used to carry out the solutions of this equation and then the solitary wave ansatz method will be used to obtain a 1-soliton solution of this equation. Finally, the invariance and multiplier approach will be applied to recover a few of the conserved quantities of this equation.

Acknowledgements

The third author (Marko D. Petković) gratefully acknowledges support from research project 144011 of the Serbian Ministry of Science. The research of the fourth author (AB) was fully supported by an NSF-CREST Grant (No. HRD-0630388) and the support is genuinely and sincerely appreciated.

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