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

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

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 240, issue C, 953-967

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.

Keywords: Rogue waves; N-solitons; Hirota method; KP equation; Bilinear form (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:240:y:2026:i:c:p:953-967

DOI: 10.1016/j.matcom.2025.08.021

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