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Solving soliton equations with self-consistent sources by method of variation of parameters |
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| Authors: | Hongxia Wu Xiaojun Liu Yunbo Zeng |
| Institution: | a Department of Mathematics, School of Science, Jimei University, Xiamen 361021, PR China b Department of Applied Mathematics, China Agriculture University, Beijing 100083, PR China c Department of Mathematical Sciences, Tsinghua University, Beijing 100084, PR China |
| Abstract: | Starting from the solutions of soliton equations and corresponding eigenfunctions obtained by Darboux transformation, we present a new method to solve soliton equations with self-consistent sources (SESCS) based on method of variation of parameters. The KdV equation with self-consistent sources (KdVSCS) is used as a model to illustrate this new method. In addition, we apply this method to construct some new solutions of the derivative nonlinear Schrödinger equation with self-consistent sources (DNLSSCS) such as phase solution, dark soliton solution, bright soliton solution and breather-type solution. |
| Keywords: | Method of variation of parameters Darboux transformation Soliton equation with self-consistent sources KdV equation with self-consistent sources Derivative nonlinear Schrö dinger equation with self-consistent sources Solution |
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