Darboux Transformation and Explicit Solutions for Discretized Modified Korteweg-de Vries Lattice Equation |
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| Authors: | WEN Xiao-Yong GAO Yi-Tian |
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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.Department of Mathematics, College of Sciences, Beijing Information;Science and Technology University, Beijing 100192, China;3.State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China |
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| Abstract: | The modified Korteweg-de Vries (mKdV) typed equations can be used todescribe certain nonlinear phenomena in fluids, plasmas, and optics. In this paper, the discretized mKdV lattice equation is investigated. With the aid of symbolic computation, the discrete matrix spectral problem for that system is constructed. Darboux transformation for that system is established based on the resulting spectral problem. Explicit solutions are derived via the Darbouxtransformation. Structures of those solutions are shown graphically, which might be helpful to understand some physical processes in fluids, plasmas, and optics. |
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| Keywords: | Darboux transformation discretized modified Korteweg-de Vries lattice equation explicit solutions symbolic computation |
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