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Generalized (2+1)-dimensional Gardner model: bilinear equations, Bäcklund transformation, Lax representation and interaction mechanisms

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Abstract

In the present paper, with symbolic computation, a generalized (2+1)-dimensional Gardner model with t dependence is directly studied without any reductions into constant-coefficient form. Integrable properties are investigated, which mainly include the bilinear equations, bilinear Bäcklund transformation, Lax representation and analytic solutions. Dynamic properties and interaction mechanisms (inelastic compression/amplification interactions) for the shock waves are also revealed by means of the asymptotic analysis and graphical simulations.

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing, 100876, China

    Xing Lü, Bo Tian, Hai-Qiang Zhang, Tao Xu & He Li

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

    Bo Tian

  3. Key Laboratory of Information Photonics and Optical Communications, Ministry of Education, Beijing University of Posts and Telecommunications, P.O. Box 128, Beijing, 100876, China

    Bo Tian

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  1. Xing Lü
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  2. Bo Tian
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  3. Hai-Qiang Zhang
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  4. Tao Xu
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  5. He Li
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Correspondence to Bo Tian.

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Lü, X., Tian, B., Zhang, HQ. et al. Generalized (2+1)-dimensional Gardner model: bilinear equations, Bäcklund transformation, Lax representation and interaction mechanisms. Nonlinear Dyn 67, 2279–2290 (2012). https://doi.org/10.1007/s11071-011-0145-9

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