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<p>This work pioneers the study of a (3+1)-dimensional Hirota-type equation, exploring its capability to model intricate wave phenomena. The equation’s relevance extends across fluid dynamics, nonlinear optics, and shallow water wave investigations. Firstly, all possible symmetry generators are determined through Lie symmetry analysis. These generators are then used to transform the given model into an ordinary differential equation. Secondly, a comprehensive array of optical soliton solutions, including dark, bright, periodic-singular, and hybrid soliton of bright and singular, has been established under defined constraints through the analytical approach introduced by Sandeep and Sachin. After that, dynamical system analysis is explored through bifurcation transitions and chaotic behavior. Tools such as Time series, Lyapunov exponents, Phase portraits, Power spectrum, and Poincaré maps facilitated the study of chaotic phenomena. Furthermore, the dynamical behavior of the obtained solutions is asserted through phase portraits. The findings accentuate the adaptability and precision of the offered solutions, reported here for the first time, laying the foundation for advances in mathematical physics and nonlinear dynamics.</p>

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A deep analytical investigation of solitons and nonlinear dynamics in the (3+1)-dimensional hirota-type equation

  • 期刊论文

  • 发表日期：

    2025年7月17日

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  • Nauman Raza,
  • Maria Luz Gandarias,
  • Muhammad Hamza Rafiq,
  • Zainab Rana,
  • Taseer Muhammad

摘要

This work pioneers the study of a (3+1)-dimensional Hirota-type equation, exploring its capability to model intricate wave phenomena. The equation’s relevance extends across fluid dynamics, nonlinear optics, and shallow water wave investigations. Firstly, all possible symmetry generators are determined through Lie symmetry analysis. These generators are then used to transform the given model into an ordinary differential equation. Secondly, a comprehensive array of optical soliton solutions, including dark, bright, periodic-singular, and hybrid soliton of bright and singular, has been established under defined constraints through the analytical approach introduced by Sandeep and Sachin. After that, dynamical system analysis is explored through bifurcation transitions and chaotic behavior. Tools such as Time series, Lyapunov exponents, Phase portraits, Power spectrum, and Poincaré maps facilitated the study of chaotic phenomena. Furthermore, the dynamical behavior of the obtained solutions is asserted through phase portraits. The findings accentuate the adaptability and precision of the offered solutions, reported here for the first time, laying the foundation for advances in mathematical physics and nonlinear dynamics.