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In this work, the \((3+1)\) -dimensional extended Sakovich equation has been solved analytically by employing the Paul-Painlevé approach method. First, the governing equation has been converted into the nonlinear ODE by using the suitable wave transformation. Then, the Paul-Painlevé approach method has been applied to obtain the new abundant analytical solutions. The solutions yield distinct wave structures for different parametric values. Bell-shaped, anti bell-shaped, and complex periodic wave solutions are obtained and illustrated through graphical representations. The obtained solutions are useful in describing various nonlinear phenomena in the field of fluid dynamics.

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Paul-Painlevé Approach to Solve \((3+1)\) -Dimensional Extended Sakovich Equation Arising in Fluid Dynamics

  • 会议论文

  • 发表日期：

    2025年

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  • Shailendra Singh,
  • B. Sagar,
  • S. Saha Ray

摘要

In this work, the \((3+1)\) -dimensional extended Sakovich equation has been solved analytically by employing the Paul-Painlevé approach method. First, the governing equation has been converted into the nonlinear ODE by using the suitable wave transformation. Then, the Paul-Painlevé approach method has been applied to obtain the new abundant analytical solutions. The solutions yield distinct wave structures for different parametric values. Bell-shaped, anti bell-shaped, and complex periodic wave solutions are obtained and illustrated through graphical representations. The obtained solutions are useful in describing various nonlinear phenomena in the field of fluid dynamics.