Exact solutions of KdV equation with time-dependent coefficients |
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| Authors: | AG Johnpillai Anjan Biswas |
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| Institution: | a International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa
b 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, USA |
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| Abstract: | In this paper, we study the Korteweg-de Vries (KdV) equation having time dependent coefficients from the Lie symmetry point of view. We obtain Lie point symmetries admitted by the equation for various forms for the time-dependent coefficients. We use the symmetries to construct the group-invariant solutions for each of the cases of the arbitrary coefficients. Subsequently, the 1-soliton solution is obtained by the aid of solitary wave ansatz method. It is observed that the soliton solution will exist provided that these time-dependent coefficients are all Riemann integrable. |
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| Keywords: | Solitons Lie symmetries Integrability |
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