Infinite Sequence of Conservation Laws and Analytic Solutions for a Generalized Variable-Coefficient Fifth-Order Korteweg-de Vries Equation in Fluids |
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| Authors: | YU Xin GAO Yi-Tian SUN Zhi-Yuan LIU Ying |
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| Affiliation: | 1.Ministry-of-Education Key Laboratory of Fluid Mechanics and National;Laboratory for Computational Fluid Dynamics, Beijing University of;Aeronautics and Astronautics, Beijing 100191, China;2.State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China |
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| Abstract: | In this paper, an infinite sequence of conservation laws for a generalized variable-coefficient fifth-order Korteweg-de Vries equation in fluids are constructed based on the Bäcklund transformation. Hirota bilinear form and symbolic computation are applied to obtain three kinds of solutions. Variablecoefficients can affect the conserved density, associated flux, andappearance of the characteristic lines. Effects of the wave number on the soliton structures are also discussed and types of soliton structures, e.g., the double-periodic soliton, parallel soliton and soliton complexes, are presented. |
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| Keywords: | variable-coefficient fifth-order Korteweg-de Vries equation in fluids infinite sequence of conservation laws Hirota bilinear method soliton solutions wave number symbolic computation |
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