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<p>Examining the exact soliton solutions of the modified Korteweg-de Vries-Kadomtsev-Petviashvili (KDV-KP) equation is the subject of this article. The studied equation, which manages the physical propagation of waves, explicitly describes how nonlinearity and dispersion can generate complex and captivating wave phenomena, such as solitary waves and wave turbulence. The equations discussed herein find practical applications in fluid dynamics when applied to simulate shallow water waves, including those encountered in rivers and tsunamis; astrophysical plasmas and fusion reactors; and nonlinear optics, where they are employed to analyse the propagation of light through nonlinear media, including optical fibres. Solitons find application in diverse domains, such as optical communications (for misdirected transmission of information over vast distances) and fluid dynamics (to simulate the behavior of long-lasting ocean waves). A wide range of exact analytical wave solutions with mixed, bright, dark, singular, and hybrid solitonic forms has been obtained using the application of the modified Sardar subequation approach and modified generalized Riccati equation mapping method. The novelty of this work lies in the application of the our proposed advanced methods to obtain diverse exact traveling wave solutions of the considered model. Using these techniques, several new families of analytical solutions–including bright, dark, singular, mixed, and hybrid soliton structures–are constructed and verified, demonstrating the effectiveness of the proposed approaches for solving nonlinear evolution equations. The accuracy of all derived solutions is checked using a direct substitution into the field equation using a Mathematica software package. Moreover, contour plots and 2D and 3D plots will be shown for a variety of parameter choices to further identify and explain the nature and behavior of these derived solutions, thus emphasizing and validating the accuracy and efficiency of this technique. We anticipate that our work will be helpful for a large number of engineering models and other related problems.</p>

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Diversity of wave structures to the fractional modified Korteweg-de Vries-Kadomtsev-Petviashvili equation

  • 期刊论文

  • 发表日期：

    2026年6月29日

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  • J. Muhammad,
  • U. Younas,
  • S. U. Rehman,
  • U. Demirbilek,
  • M. A. Hosseinzadeh,
  • H. Rezazadeh

摘要

Examining the exact soliton solutions of the modified Korteweg-de Vries-Kadomtsev-Petviashvili (KDV-KP) equation is the subject of this article. The studied equation, which manages the physical propagation of waves, explicitly describes how nonlinearity and dispersion can generate complex and captivating wave phenomena, such as solitary waves and wave turbulence. The equations discussed herein find practical applications in fluid dynamics when applied to simulate shallow water waves, including those encountered in rivers and tsunamis; astrophysical plasmas and fusion reactors; and nonlinear optics, where they are employed to analyse the propagation of light through nonlinear media, including optical fibres. Solitons find application in diverse domains, such as optical communications (for misdirected transmission of information over vast distances) and fluid dynamics (to simulate the behavior of long-lasting ocean waves). A wide range of exact analytical wave solutions with mixed, bright, dark, singular, and hybrid solitonic forms has been obtained using the application of the modified Sardar subequation approach and modified generalized Riccati equation mapping method. The novelty of this work lies in the application of the our proposed advanced methods to obtain diverse exact traveling wave solutions of the considered model. Using these techniques, several new families of analytical solutions–including bright, dark, singular, mixed, and hybrid soliton structures–are constructed and verified, demonstrating the effectiveness of the proposed approaches for solving nonlinear evolution equations. The accuracy of all derived solutions is checked using a direct substitution into the field equation using a Mathematica software package. Moreover, contour plots and 2D and 3D plots will be shown for a variety of parameter choices to further identify and explain the nature and behavior of these derived solutions, thus emphasizing and validating the accuracy and efficiency of this technique. We anticipate that our work will be helpful for a large number of engineering models and other related problems.