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Wronskian solutions and integrability for a generalized variable-coefficient forced Korteweg–de Vries equation in fluids

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Abstract

Under investigation in this paper is a generalized variable-coefficient forced Korteweg–de Vries equation, which can describe the shallow-water waves, internal gravity waves, and so on. With symbolic computation, the soliton solutions in the Wronskian form are derived based on the given bilinear form. Bäcklund transformation and Lax pair for such equation are also constructed. Variable coefficients and parameters of three solitons are managed to observe the features of the solitonic propagation and interaction, e.g., the solitonic velocity, amplitude and background. Our results could be expected to benefit the relevant problems in fluids.

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Authors and Affiliations

  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

    Xin Yu, Yi-Tian Gao, Zhi-Yuan Sun & Ying Liu

  2. State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    Yi-Tian Gao

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  1. Xin Yu
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  2. Yi-Tian Gao
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  3. Zhi-Yuan Sun
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  4. Ying Liu
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Correspondence to Yi-Tian Gao.

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Yu, X., Gao, YT., Sun, ZY. et al. Wronskian solutions and integrability for a generalized variable-coefficient forced Korteweg–de Vries equation in fluids. Nonlinear Dyn 67, 1023–1030 (2012). https://doi.org/10.1007/s11071-011-0044-0

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