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Bifurcation soliton solutions, M-lump, breather waves, and interaction solutions for (3+1)-dimensional P-type equation

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  • Wang, Tianlin
  • Tian, Lin
  • Ma, Zhimin
  • Yang, Zhuodong
  • Han, Hongwei

Abstract

In this paper, we employ the Bell polynomial to derive the Hirota bilinear form and obtain multi-soliton solutions using the Hirota bilinear method. Based on the multi-soliton solutions, we derive the resonant Y-type soliton, the heterotypic soliton, and the X-type soliton by setting the partial dispersion coefficient to zero. Additionally, the M-lump wave solutions are constructed using the long-wave limit method, and their various characteristics, as well as the collision phenomena of the 2-lump and 3-lump solutions, are analyzed. Breather waves are derived as well, using the complex conjugation method. Finally, we study the interaction solutions and observe that their collision is elastic, demonstrated them through figures. These solutions have broad applications in nonlinear science, enhancing our understanding of related physical phenomena and contributing to an in-depth investigation of complex nonlinear problems.

Suggested Citation

  • Wang, Tianlin & Tian, Lin & Ma, Zhimin & Yang, Zhuodong & Han, Hongwei, 2025. "Bifurcation soliton solutions, M-lump, breather waves, and interaction solutions for (3+1)-dimensional P-type equation," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:chsofr:v:192:y:2025:i:c:s096007792401484x
    DOI: 10.1016/j.chaos.2024.115932
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    References listed on IDEAS

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    1. Zhang, Run-Fa & Li, Ming-Chu & Gan, Jian-Yuan & Li, Qing & Lan, Zhong-Zhou, 2022. "Novel trial functions and rogue waves of generalized breaking soliton equation via bilinear neural network method," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    2. Li, Li & Yu, Fajun, 2024. "The fourth-order dispersion effect on the soliton waves and soliton stabilities for the cubic-quintic Gross–Pitaevskii equation," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    3. He, Xue-Jiao & Lü, Xing, 2022. "M-lump solution, soliton solution and rational solution to a (3+1)-dimensional nonlinear model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 327-340.
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