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Novel evolutionary behaviors of \(\pmb {N}\)-soliton solutions for the (3+1)-dimensional generalized Camassa–Holm–Kadomtsev–Petciashvili equation

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Abstract

Under investigation in this work is to explore novel evolutionary behaviors of N-soliton solutions for the (3+1)-dimensional generalized Camassa–Holm–Kadomtsev–Petciashvili (gCH-KP) equation, which is proposed to describe the role of dispersion in the formation of patterns in liquid drops. Resonant soliton solutions composed of soliton molecules and Y-type soliton solutions are constructed by introducing appropriate condition to N-soliton solutions. High-order breather solutions are generated with the complex conjugate relation of the parameters of N-soliton solutions, and rational breather solution is obtained by breather limit method. Moreover, a variety of hybrid solutions are derived by combining with resonant condition, long-wave limit approach and parameter complexification method, which contain soliton molecule, Y-type soliton, high-order breathers, lump soliton and their interaction diagrams are simulated explicitly. These received results greatly enrich the solutions and nonlinear dynamical behaviors of gCH-KP equation, and it could be helpful for understanding in nonlinear partial differential equation deeply.

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The authors declare that data supporting the findings of this study are available within the article, and the figures are concrete expression.

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Funding

This work is supported by National Natural Science Foundation of China (Grant No. 12261076, 12261075), Scientific and Technological Innovation Team of Nonlinear Analysis and Algebra with Their Applications in Universities of Yunnan Province (Grant No. 2020CXTD25), Yunnan Fundamental Research Projects (Grant Nos. 202201AT070018, 202105AC160087, 202305AC160005, 202001BA070001-32, 202101BA070001-280), and Scientific Research Fund Project of Education Department of Yunnan Province (Grant No. 2023J1031).

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Authors and Affiliations

  1. Key Laboratory of Analytical Mathematics and Intelligent Computing for Yunnan Provincial Department of Education and School of Mathematics and Statistics, Qujing Normal University, Qujing, 655011, China

    Longxing Li & Bitao Cheng

  2. School of Mathematics and Statistics, Yunnan University, Kunming, 650091, China

    Zhengde Dai

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  1. Longxing Li
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Li, L., Cheng, B. & Dai, Z. Novel evolutionary behaviors of \(\pmb {N}\)-soliton solutions for the (3+1)-dimensional generalized Camassa–Holm–Kadomtsev–Petciashvili equation. Nonlinear Dyn 112, 2157–2173 (2024). https://doi.org/10.1007/s11071-023-09122-1

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