A Generalized Algebraic Method for Constructing a Series of Explicit Exact Solutions of a (1+1)-Dimensional Dispersive Long Wave Equation |
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| Authors: | CHEN Yong WANG Qi LI Biao |
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| Institution: | Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China;Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;Key Laboratory of Mathematics and Mechanization, the Chinese Academy of Sciences, Beijing 100080, China Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;Key Laboratory of Mathematics and Mechanization, the Chinese Academy of Sciences, Beijing 100080, China Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;Key Laboratory of Mathematics and Mechanization, the Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | Making use of a new and more general ansatz, we present the generalized algebraic method to uniformlyconstruct a series of new and general travelling wave solution for nonlinear partial differential equations. As an applicationof the method, we choose a (1 1)-dimensional dispersive long wave equation to illustrate the method. As a result, wecan successfully obtain the solutions found by the method proposed by Fan E. Fan, Comput. Phys. Commun. 153 (2003)17] and find other new and more general solutions at the same time, which include polynomial solutions, exponentialsolutions, rational solutions, triangular periodic wave solutions, hyperbolic and soliton solutions, Jacobi and Weierstrassdoubly periodic wave solutions. |
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| Keywords: | generalized algebraic method symbolic computation solitary wave solution Weierstrass andJacobi elliptic functions periodic solution |
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