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<p>In this work, we examine the dynamic behaviors of the fractional modified Korteweg-de Vries-Kadomtsev-Petviashvili equation. The equation provides a physical explanation for wave propagation, clarifying how nonlinearity and dispersion may result in complex wave phenomena like turbulence and solitary waves. This equation is utilized in ocean engineering, fluid dynamics, and shallow water waves, focusing on shallow water wave modeling in tsunamis and river waves. Many solutions, including hyperbolic, periodic, and exponential function solutions, as well as dark, combined solitons, and singular, are secured using the analytical techniques namely extended sinh-Gordon equation expansion approach, Riccati modified extended simple equation technique, and new modified generalized exponential rational function approach. Moreover, a variety of graphs are sketched by the assistance of the suitable parameters. Furthermore, multistability analysis is also under investigation in this study. The suggested techniques are certainly the most simple, efficient, and beneficial for tackling a variety of nonlinear models found in applied physics and mathematics, aiming to provide a range of exact solutions. The derived solutions are crucial due to their compatibility in the field of ocean mechanics.</p>

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Wave propagation and multistability analysis to the modified fractional KDV-KP equation in diversity of fields

  • 期刊论文

  • 发表日期：

    2025年5月27日

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  • Jan Muhammad,
  • Usman Younas

摘要

In this work, we examine the dynamic behaviors of the fractional modified Korteweg-de Vries-Kadomtsev-Petviashvili equation. The equation provides a physical explanation for wave propagation, clarifying how nonlinearity and dispersion may result in complex wave phenomena like turbulence and solitary waves. This equation is utilized in ocean engineering, fluid dynamics, and shallow water waves, focusing on shallow water wave modeling in tsunamis and river waves. Many solutions, including hyperbolic, periodic, and exponential function solutions, as well as dark, combined solitons, and singular, are secured using the analytical techniques namely extended sinh-Gordon equation expansion approach, Riccati modified extended simple equation technique, and new modified generalized exponential rational function approach. Moreover, a variety of graphs are sketched by the assistance of the suitable parameters. Furthermore, multistability analysis is also under investigation in this study. The suggested techniques are certainly the most simple, efficient, and beneficial for tackling a variety of nonlinear models found in applied physics and mathematics, aiming to provide a range of exact solutions. The derived solutions are crucial due to their compatibility in the field of ocean mechanics.