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Novel soliton molecules and wave interactions for a (3 + 1)-dimensional nonlinear evolution equation

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Abstract

New wave excitations are revealed for a (3 + 1)-dimensional nonlinear evolution equation to enrich nonlinear wave patterns in nonlinear systems. Based on a new variable separation solution with two arbitrary variable separated functions obtained by means of the multilinear variable separation approach, localized excitations of N dromions, \(N\times M\) lump lattice and ring soliton lattice are constructed. In addition, it is observed that soliton molecules can be composed of diverse “atoms” such as the dromions, lumps and ring solitons, respectively. Elastic interactions between solitons and soliton molecules are graphically demonstrated.

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Acknowledgements

The authors acknowledge the financial support by the National Natural Science Foundation of China (No. 11675055) and the Science and Technology Commission of Shanghai Municipality (No. 18dz2271000).

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200062, China

    Xiao-yan Tang

  2. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China

    Chao-jie Cui

  3. Department of Physics, Hangzhou Normal University, Hangzhou, 310036, China

    Zu-feng Liang

  4. School of Computer Science and Technology, Shanghai Normal University, Shanghai, 200234, China

    Wei Ding

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  1. Xiao-yan Tang
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  2. Chao-jie Cui
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  3. Zu-feng Liang
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  4. Wei Ding
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Correspondence to Xiao-yan Tang or Zu-feng Liang.

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Tang, Xy., Cui, Cj., Liang, Zf. et al. Novel soliton molecules and wave interactions for a (3 + 1)-dimensional nonlinear evolution equation. Nonlinear Dyn 105, 2549–2557 (2021). https://doi.org/10.1007/s11071-021-06687-7

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  • DOI: https://doi.org/10.1007/s11071-021-06687-7

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