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Resonance \(\varvec{Y}\)-type soliton, hybrid and quasi-periodic wave solutions of a generalized \(\varvec{(2+1)}\)-dimensional nonlinear wave equation

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Abstract

In this paper, we consider a generalized \((2+1)\)-dimensional nonlinear wave equation. Based on the bilinear method, the N-soliton solutions are obtained. The resonance Y-type soliton, which is similar to the capital letter Y in the spatial structure, and the interaction solutions between different types of resonance solitons are constructed by adding some new constraints to the parameters of the N-soliton solutions. The new type of two-opening resonance Y-type soliton solutions is presented by choosing some appropriate parameters in 3-soliton solutions. The hybrid solutions consisting of resonance Y-type solitons, breathers and lumps are investigated. The trajectories of the lump waves before and after the collision with the resonance Y-type solitons are analyzed from the perspective of mathematical mechanism. Furthermore, the multi-dimensional Riemann-theta function is employed to investigate the quasi-periodic wave solutions. The one-periodic and two-periodic wave solutions are obtained. The asymptotic properties are systematically analyzed, which establish the relations between the quasi-periodic wave solutions and the soliton solutions. The results may be helpful to provide some effective information to analyze the dynamical behaviors of solitons, fluid mechanics, shallow water waves and optical solitons.

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Acknowledgements

This work is supported by Shanxi Province Science Foundation for Youths (No. 201901D211274), Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (No. 2019L0531), Research Project Supported by Shanxi Scholarship Council of China (No. 2020-105) and the Fund for Shanxi “1331KIRT.”

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  1. College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan, 030024, Shanxi, People’s Republic of China

    Lingchao He

  2. College of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, Shanxi, People’s Republic of China

    Jianwen Zhang

  3. Department of Mathematics, North University of China, Taiyuan, 030051, Shanxi, People’s Republic of China

    Zhonglong Zhao

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  1. Lingchao He
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He, L., Zhang, J. & Zhao, Z. Resonance \(\varvec{Y}\)-type soliton, hybrid and quasi-periodic wave solutions of a generalized \(\varvec{(2+1)}\)-dimensional nonlinear wave equation. Nonlinear Dyn 106, 2515–2535 (2021). https://doi.org/10.1007/s11071-021-06922-1

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