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<p>This work investigates the nonlinear dynamics and exact soliton solutions of the (3+1)-dimensional Sakovich equation (3D-SE), an integrable model with broad applications in fluid dynamics and multidimensional nonlinear wave phenomena. The 3D-SE characterizes the multidirectional propagation of nonlinear waves, enabling a realistic representation of complex physical systems. To obtain analytical insights, we apply the modified Sardar sub-equation method (mSSEM), which yields a diverse form of exact solutions, including solitary waves, kink-type solitons, and periodic wave structures. The effectiveness of the mSSEM lies in its systematic handling of nonlinearities and its capability to construct closed-form solutions. A detailed bifurcation analysis is performed to examine the qualitative behavior of the solutions under varying parametric conditions. The obtained results are validated through symbolic computations in Mathematica and visualized using comprehensive graphical simulations, demonstrating the physical characteristics and stability of the solitons. Additionally, modulational instability analysis is carried out to further confirm the exactness and physical relevance of the solutions. Overall, this study enhances the understanding of the integrability and diverse solution structure of the 3D-SE, offering valuable insights into higher-dimensional nonlinear partial differential equations arising in fluid dynamics.</p>

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Stability, soliton dynamics, and bifurcation analysis of the (3+1)-dimensional Sakovich equation in fluid dynamics

  • 期刊论文

  • 发表日期：

    2025年7月22日

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  • Muhammad Arshad,
  • Khurrem Shehzad,
  • Mustafa Bayram,
  • Muhammad Farman,
  • Aceng Sambas

摘要

This work investigates the nonlinear dynamics and exact soliton solutions of the (3+1)-dimensional Sakovich equation (3D-SE), an integrable model with broad applications in fluid dynamics and multidimensional nonlinear wave phenomena. The 3D-SE characterizes the multidirectional propagation of nonlinear waves, enabling a realistic representation of complex physical systems. To obtain analytical insights, we apply the modified Sardar sub-equation method (mSSEM), which yields a diverse form of exact solutions, including solitary waves, kink-type solitons, and periodic wave structures. The effectiveness of the mSSEM lies in its systematic handling of nonlinearities and its capability to construct closed-form solutions. A detailed bifurcation analysis is performed to examine the qualitative behavior of the solutions under varying parametric conditions. The obtained results are validated through symbolic computations in Mathematica and visualized using comprehensive graphical simulations, demonstrating the physical characteristics and stability of the solitons. Additionally, modulational instability analysis is carried out to further confirm the exactness and physical relevance of the solutions. Overall, this study enhances the understanding of the integrability and diverse solution structure of the 3D-SE, offering valuable insights into higher-dimensional nonlinear partial differential equations arising in fluid dynamics.