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Lax pair, Darboux transformation and soliton solutions for the (2+1)-dimensional generalization of shallow water wave equation
Wen Xiaoyong 1 #,Gao Yitian 2 *
1.Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191
2.Ministry-of-Education Key Laboratory of Fluid Mechanics andNational Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191
*Correspondence author
#Submitted by
Subject:
Funding: by the Fundamental Research Funds for the Central Universities of China(No.No.2011BUPTYB02), the Specialized Research Fund for the Doctoral Program of Higher Education (No.No. 200800130006), Chinese Ministry of Education, and by the Scientific Research Common Profram of Beijing Municipal Commission of Education(No.No.KM201010772020), National Natural Science Foundation of China(No.No.60772023)
Opened online:18 May 2012
Accepted by: none
Citation: Wen Xiaoyong,Gao Yitian.Lax pair, Darboux transformation and soliton solutions for the (2+1)-dimensional generalization of shallow water wave equation[OL]. [18 May 2012] http://en.paper.edu.cn/en_releasepaper/content/4478206
 
 
In this paper, the (2+1)-dimensional generalization of shallow water wave equation which can be used to describe the propagation of ocean waves is analytically investigated. With the aid of symbolic computation, we prove that the (2+1)-dimensional generalization of shallow water wave equation has the Painlev'e property under a certain condition and apply the singular manifold method to constructing its Lax pair. Based on the obtained Lax representation, the Darboux transformation is constructed. The first iterated solution, second iterated solution and an N-soliton solution with an arbitrary function are derived with the resulting Darboux transformation. Relevant properties are graphically illustrated, which might be helpful to understanding the propagation processes for ocean waves on shallow waters.
Keywords:NThe (2+1)-dimensional generalization of shallow water wave equation; the singular manifold method; Lax pair; Darboux transformation; Symbolic computation
 
 
 

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