Modulation Instability, N-Solitons, Resonant Multi-Wave Structures and Other Diverse Interaction Phenomena to the (2+1)-Dimensional Kadomtsev-Petviashvili-BenjaminBona-Mahony Equation

• Muhammad Naveed Rafiq ^[1] ; Haibo Chen ^[1]
  1. [1] Central South University

     Central South University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 1, 2025
• Idioma: inglés
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• Resumen

  • Nonlinear science is a key area of scientific research dedicated to studying the fundamental properties and common features of nonlinear phenomena. This study specifically investigates the (2+1)-dimensional Kadomtsev-Petviashvili-BenjaminBona-Mahony (KP-BBM) equation in nonlinear dispersive systems. By employing the Hirota bilinear method along with the linear superposition principle to the bilinear form of this equation, various new wave structures are effectively derived, such as N-solitons, resonance-type solitons, hybrid interaction solutions, and resonant multiwave solutions. To ensure the physical compatibility of the results, we generated 3D and density plots using appropriate parametric values, which will provide effective insights into the obtained wave solutions. Moreover, we provide a modulation instability analysis of the KP-BBM equation with its stability region. The novelty of this work lies in the fact that the results discussed are new and have not been previously explored for the given equation. Additionally, the methods applied are efficient and reliable for constructing new soliton wave solutions in nonlinear physical phenomena.

    We predict that the findings of this study will have significant applications in optical fibers, plasma physics, engineering and fluid dynamics.