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Darboux Transformation and Soliton Solutions for the (2+1)-Dimensional Generalization of Shallow Water Wave Equation with Symbolic Computation

Darboux Transformation and Soliton Solutions for the (2+1)-Dimensional Generalization of Shallow Water Wave Equation with Symbolic Computation
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摘要 In this paper, the (2+l)-dimensional generalization of shallow water wave equation, which may be used to describe the propagation of ocean waves, is analytically investigated. With the aid of symbolic computation, we prove that the (2+ l)-dimensional generalization of shallow water wave equation possesses the Palnlev6 property under a certain condition, and its Lax pair is constructed by applying the singular manifold method. Based on the obtained Lax representation, the Darboux transformation (DT) is constructed. The first iterated solution, second iterated solution and a special N-soliton solution with an arbitrary function are derived with the resulting DT. Relevant properties are graphically illustrated, which might be helpful to understanding the propagation processes for ocean waves in shallow water.
出处 《Communications in Theoretical Physics》 SCIE CAS CSCD 2013年第8期194-200,共7页 理论物理通讯(英文版)
基金 Supported by the National Natural Science Foundation of China under Grant No.61072145 the Scientific Research Common Program of Beijing Municipal Commission of Education under Grant No.SQKM201211232016
关键词 (2+1)-dimensional generalization of shallow water wave equation singular manifold method Laxpair Darboux transformation symbolic computation 浅水波方程 符号计算 孤子解 广义 达布变换 Darboux变换 传播过程 Lax表示
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