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

作     者：闻小永 孟祥花 

作者机构：Department of MathematicsSchool of Applied ScienceBeijing Information Science and Technology University 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2013年第60卷第8期

页      面：194-200页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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 

主　　题：(2+1)-dimensional generalization of shallow water wave equation singular manifold method Laxpair Darboux transformation symbolic computation 

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.