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Analysis and simulations of center-controlled rogue waves in higher-order BKP equation with novel multiple order kink soliton interactions

Author

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  • Algolam, Mohamed S.
  • Aldwoah, Khaled
  • Hassan, Mohammed
  • Mustafa, Alaa
  • Muflh, Blgys
  • Ahmad, Shabir

Abstract

In this manuscript, we examine a (3＋1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation, illustrating an advanced extension of the classical KP equation. Via symbolic computation, we derive rogue wave (RW) solutions governed by the center-controlled parameters τ and κ. The bilinear form of the equation is formulated by transforming the dependent variable u and introducing an auxiliary function (AF) f defined in terms of transformed variables μ and ν. Using Hirota’s method, we construct first-, second-, and third-order RW solutions by tuning the center-controlled parameters and exploiting the generalized N-soliton equation. Moreover, we investigate the novel interactions between center-controlled RWs and multiple-order kink solitons. To visualize the dynamic behavior of these interactions, we illustrate the effects of varying the center-controlled parameters on RWs and their interplay with kink solitons.

Suggested Citation

  • Algolam, Mohamed S. & Aldwoah, Khaled & Hassan, Mohammed & Mustafa, Alaa & Muflh, Blgys & Ahmad, Shabir, 2026. "Analysis and simulations of center-controlled rogue waves in higher-order BKP equation with novel multiple order kink soliton interactions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 240(C), pages 953-967.
    • Handle: RePEc:eee:matcom:v:240:y:2026:i:c:p:953-967
    DOI: 10.1016/j.matcom.2025.08.021
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    References listed on IDEAS

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    1. Agarwal, P. & Deni̇z, S. & Jain, S. & Alderremy, A.A. & Aly, Shaban, 2020. "A new analysis of a partial differential equation arising in biology and population genetics via semi analytical techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    2. Mandal, Uttam Kumar & Malik, Sandeep & Kumar, Sachin & Zhang, Yi & Das, Amiya, 2024. "Integrability aspects, rational type solutions and invariant solutions of an extended (3+1)-dimensional B-type Kadomtsev–Petviashvili equation," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    3. Khadijo Rashid Adem & Chaudry Masood Khalique, 2013. "Exact Solutions and Conservation Laws of a (2+1)-Dimensional Nonlinear KP-BBM Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-5, April.
    4. Khadijo Rashid Adem & Chaudry Masood Khalique, 2013. "Exact Solutions and Conservation Laws of a (2+1)‐Dimensional Nonlinear KP‐BBM Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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