Soliton Solution and Conservation Law of Gear-Grimshaw Model for Shallow Water Waves

H. Trikia, A.H. Karab, A.H. Bhrawyc,d and A. Biswase,c aRadiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, P.O. Box 12, 23000 Annaba, Algeria bSchool of Mathematics, Centre for Differential Equations Continuum Mechanics and Applications, University of the Witwatersrand, Johannesburg, Wits 2050, South Africa cDepartment of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia dDepartment of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt eDepartment of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA

Received: December 4, 2013

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This paper is going to obtain the soliton solution of the Gear-Grimshaw model that describes the dynamics of two-layered shallow water waves in oceans and rivers. The topological 1-soliton solution will be obtained by the ansatz method. There are several constraint conditions that will be taken care of. This will be followed by the model with power law nonlinearity. Subsequently, the conservation laws for this model will be derived by the aid of multiplier approach from the Lie symmetry analysis. Finally, the F-expansion method will extract a few more interesting solutions to the model.

DOI: 10.12693/APhysPolA.125.1099 PACS numbers: 02.30.Ik, 02.30.Jr, 47.35.Fg