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Resonance Y-shape solitons and mixed solutions for a (2+1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics

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Abstract

Under the well-known bilinear method of Hirota, the specific expression for N-soliton solutions of (2+1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada(gCDGKS) equation in fluid mechanics is given. By defining a novel restrictive condition on N-soliton solutions, resonant Y-type and X-type soliton solutions are generated. Under the new proposed constraint, combined with the velocity resonance method and module resonant method, the mixed solutions of resonant Y-type solitons and line waves and breather solutions are found. Finally, with the support of long-wave limit method, the interaction between resonant Y-type solitons and higher-order lumps is shown, and the motion trajectory equation before and after the interaction between lumps and resonant Y-type solitons is derived. These new results greatly extend the exact solution of (2+1)-dimensional gCDGKS equation already available in the literature and provide new ideas for studying the dynamical behaviors of fluid mechanic, soliton and shallow water wave and so on.

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Acknowledgements

The work is supported by the National Natural Science Foundation of China (project No. 11371086, 11671258, 11975145), the Fund of Science and Technology Commission of Shanghai Municipality (project No. 13ZR1400100), the Fund of Donghua University, institute for nonlinear sciences and the Fundamental Research Funds for the Central Universities with contract number 2232021G-13.

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  1. Department of Applied Mathematics, Donghua University, Shanghai, 201620, China

    Hongcai Ma, Shupan Yue & Aiping Deng

  2. Institute for Nonlinear Sciences, Donghua University, Shanghai, 201620, China

    Hongcai Ma & Aiping Deng

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Ma, H., Yue, S. & Deng, A. Resonance Y-shape solitons and mixed solutions for a (2+1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics. Nonlinear Dyn 108, 505–519 (2022). https://doi.org/10.1007/s11071-022-07205-z

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