Lax Pair and Darboux Transformation for a Variable-Coefficient Fifth-Order Korteweg-de Vries Equation with Symbolic Computation |
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| Authors: | ZHANG Ya-Xing ZHANG Hai-Qiang LI Juan XU Tao ZHANG Chun-Yi TIAN Bo |
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| Institution: | [1]School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China [2]Meteorology Center of Air Force Command Post, Changchun 130051, China [3]Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China [4]State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100083, China [5]Key Laboratory of Optical Communication and Lightwave Technologies, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China |
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| Abstract: | In this paper, we put our focus on a variable-coefficient fifth-order Korteweg-de Vries (fKdV) equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those
constraints, some integrable properties are derived, such as the Lax
pair and Darboux transformation. Via the Darboux transformation,
which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out. |
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| Keywords: | variable-coefficient fifth-order Korteweg-de Vries equation Lax pair Darboux transformation solitonic solutions symbolic computation |
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