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Interaction phenomena between solitons, lumps and breathers for the combined KP3-4 equation

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Abstract

The Hirota’s bilinear method is used to determine the N-soliton solutions of the combined KP3 and KP4 equation, from which the M-lump solutions that decay to zero in all directions in the plane are obtained by using long wave limit when \(N=2M\). Then, we discuss some novel hybrid solutions between lumps, breathers and solitons. In order to shade more light on the dynamical characteristics of the acquired solutions, numerical simulations have been performed by means of the 3D figures under careful choice of the values of the parameters involved. These results may be useful for understanding the propagation phenomena of nonlinear localized waves. The hybrid solutions describing molecules between lumps, breathers and solitons are also presented.

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Funding

The work is supported by National Natural Science Foundations of China No.11975204, Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ20A010009.

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Authors and Affiliations

  1. College of Science, Zhejiang University of Technology, Hangzhou, China

    Xiazhi Hao

  2. School of Computer Science, Shaanxi Normal University, Xi’an, China

    Yan Li

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  1. Xiazhi Hao
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  2. Yan Li
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Correspondence to Xiazhi Hao.

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Hao, X., Li, Y. Interaction phenomena between solitons, lumps and breathers for the combined KP3-4 equation. Nonlinear Dyn 111, 6701–6710 (2023). https://doi.org/10.1007/s11071-022-08191-y

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