New Auto-Darboux Transformation and Explicit Analytic Solutions for the Generalized KdV Equation with External Force Term
Received:October 26, 1999  
Key Words: GKdV equation   Lax pair   Darboux transformation   analytic solution   solitary wave solution.  
Fund Project:Supported by the National Natural Science Foundation of China under the Grant (19572022), Doctoral Foundation of Education Ministry of China under the Grant (98014119) and the National Key Basic Research Project under the Grant(G1998030600)
Author NameAffiliation
YAN Zhen-ya Dept. of Appl. Math.
Dalian University of Technology
ZHANG Hong-qing Dept. of Appl. Math.
Dalian University of Technology
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      In this paper, based on Lax pair of Riccati form of the generalized KdV(GKdV) equation with external force term, a new auto-Darboux transformation (ADT) is derived. As the application of the ADT, only if integration is needed, a series of explicit analytic solutions can be obtained, which contain solitary-like wave solutions. This method may be important for seeking more new and physical signficant analytic solutions of nonlinear evolution equations.
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