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Evolutionary higher-order lump–rogue waves in an integrable (3+1)-dimensional complex Kadomtsev–Petviashvili model: Insights on the dynamical patterns through explicit solutions

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  • Singh, Sudhir
  • Manikandan, K.
  • Sakkaravarthi, K.

Abstract

The rogue wave phenomenon continues to attract ever-increasing interest in both theoretical and experimental exploration, with higher-dimensional nonlinear soliton models possessing more fascinating evolutionary dynamics. This motivated the present work to study the evolutionary characteristics of lump–rogue waves in an integrable (3+1)-dimensional complex Kadomtsev–Petviashvili model with complex dispersion-nonlinearity coefficients by constructing explicit solutions through the Hirota bilinearization technique and generalized recursive polynomials. With systematic analysis of the solutions, we reveal the dynamical features and various pattern formation strategies of lump–rogue waves and provide extensive graphical demonstrations. The results are discussed elaborately with certain possible future directions. The observed results can be helpful for enhancing the understanding of localized nonlinear evolutionary waves.

Suggested Citation

  • Singh, Sudhir & Manikandan, K. & Sakkaravarthi, K., 2025. "Evolutionary higher-order lump–rogue waves in an integrable (3+1)-dimensional complex Kadomtsev–Petviashvili model: Insights on the dynamical patterns through explicit solutions," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925001821
    DOI: 10.1016/j.chaos.2025.116169
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    References listed on IDEAS

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    1. Zhao, Yu & Tian, Bo, 2023. "Gram-type, three-breather and hybrid solutions for a (3＋1)-dimensional generalized variable-coefficient shallow water wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Guo, Jutong & He, Jingsong & Li, Maohua & Mihalache, Dumitru, 2021. "Multiple-order line rogue wave solutions of extended Kadomtsev–Petviashvili equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 251-257.
    3. Zhang, Zhao & Guo, Qi & Stepanyants, Yury, 2023. "Creation of weakly interacting lumps by degeneration of lump chains in the KP1 equation," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Wazwaz, Abdul-Majid, 2024. "Breather wave solutions for an integrable (3+1)-dimensional combined pKP–BKP equation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    5. Singh, Sudhir & Sakkaravarthi, K. & Murugesan, K., 2022. "Localized nonlinear waves on spatio-temporally controllable backgrounds for a (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq model in water waves," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
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