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<p>The extended hyperbolic function method and the modified F-expansion method are two of the most potent and innovative approaches used in this work to solve the (3+1)-dimensional Boussinesq problem. The flow of shallow water waves in a surface system with modest amplitude is examined using the governing model. In this paper, new traveling wave solutions are extracted for the first time using the modified F-expansion approach and the extended hyperbolic function method. Bright solitons, dark solitons, bright and dark solitary wave solutions, periodic singular solutions, and singular solitons are examples of these traveling wave solutions. There is also a discussion of the constraint conditions that guarantee the validity of the solutions produced. For suitable parametric values, contour plots, 2D plots, and 3D surface graphics are used to describe the graphical representations of the built solutions. The dynamic features and physical importance of the proposed equation are well conveyed by these graphic representations. Additionally, modulation instability analysis is used to examine the stability of the suggested model.</p>

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Formation of solitary wave solutions to nonlinear (3+1)-dimensional Boussinesq equation via analytical techniques

  • 期刊论文

  • 发表日期：

    2025年5月9日

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  • Saima Arshed,
  • Ghazala Akram,
  • Maasoomah Sadaf,
  • Muhammad Sulaiman Riaz

摘要

The extended hyperbolic function method and the modified F-expansion method are two of the most potent and innovative approaches used in this work to solve the (3+1)-dimensional Boussinesq problem. The flow of shallow water waves in a surface system with modest amplitude is examined using the governing model. In this paper, new traveling wave solutions are extracted for the first time using the modified F-expansion approach and the extended hyperbolic function method. Bright solitons, dark solitons, bright and dark solitary wave solutions, periodic singular solutions, and singular solitons are examples of these traveling wave solutions. There is also a discussion of the constraint conditions that guarantee the validity of the solutions produced. For suitable parametric values, contour plots, 2D plots, and 3D surface graphics are used to describe the graphical representations of the built solutions. The dynamic features and physical importance of the proposed equation are well conveyed by these graphic representations. Additionally, modulation instability analysis is used to examine the stability of the suggested model.