Darboux transformation and explicit solutions for the integrable sixth-order KdV equation for nonlinear waves |
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Authors: | Xiao-Yong Wen Yi-Tian Gao Lei Wang |
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Institution: | a Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China b Department of Mathematics, College of Sciences, Beijing Information Science and Technology University, Beijing 100192, China c State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China |
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Abstract: | Korteweg-de Vries (KdV)-type equations can describe some physical phenomena in fluids, nonlinear optics, quantum mechanics, plasmas, etc. In this paper, with the aid of symbolic computation, the integrable sixth-order KdV equation is investigated. Darboux transformation (DT) with an arbitrary parameter is presented. Explicit solutions are derived with the DT. Relevant properties are graphically illustrated, which might be helpful to understand some physical processes in fluids, plasmas, optics and quantum mechanics. |
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Keywords: | Integrable sixth-order KdV equation Lax pair Darboux transformation Explicit solution Symbolic computation |
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