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Darboux transformation and explicit solutions for the integrable sixth-order KdV equation for nonlinear waves
Authors:Xiao-Yong Wen  Yi-Tian Gao  Lei Wang
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
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.
Keywords:Integrable sixth-order KdV equation  Lax pair  Darboux transformation  Explicit solution  Symbolic computation
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