A new algebraic method for finding the line soliton solutions and doubly periodic wave solution to a two-dimensional perturbed KdV equation |
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Institution: | 1. Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India;2. Faculty of Mechanical Engineering, Technion Israel Institute of Technology, Technion City, Haifa 32000, Israel |
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Abstract: | A new algebraic method is devised to obtain a series of exact solutions for general nonlinear equations. Compared with the most existing tanh methods, the proposed method gives new and more general solutions. More importantly, the method provides a guideline to classify the various types of the solution according to some parameters. For illustration, we apply the method to solve a new two-dimensional perturbed KdV equation and successfully construct the various kind of exact solutions including line soliton solutions, rational solutions, triangular periodic solutions, Jacobi, and Weierstrass doubly periodic solutions. |
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