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<p>In this study, we utilized the modified Sardar subequation function approach to examine the (3+1)-dimensional nonlinear Gardner–Kadomtsev–Petviashvili equation, which models the nonlinear propagation of monomode wave packets exhibiting soliton solutions. The model serves as a mathematical depiction of wave characteristics and dynamics within specific physical systems. The main aim was to transform this nonlinear (3+1)-dimensional model into a second-order nonlinear ordinary differential equation through appropriate wave transformations. Our goal was to derive new, well-defined traveling wave solitons and periodic wave solutions. The results are presented in terms of exponential functions, hyperbolic trigonometric functions, and combinations of rational exponential functions with trigonometric and hyperbolic functions. These solutions reveal important features of the underlying physical phenomena and are original contributions. To fully understand the behavior of these solutions, we analyzed them through multiple graphical representations across various dimensions. Using software packages, we have thoroughly checked the validity of all the solutions we found by plugging each one into its own equation and finding that it was correct.</p>

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Analyzing soliton dynamics of the solutions of (3+1)-dimensional Gardner–Kadomtsev–Petviashvili model for pulse propagation in single-mode optical fibers

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Adnan Ahmad Mahmud,
  • Kalsum Abdulrahman Muhamad,
  • Tanfer Tanriverdi,
  • Haci Mehmet Baskonus

摘要

In this study, we utilized the modified Sardar subequation function approach to examine the (3+1)-dimensional nonlinear Gardner–Kadomtsev–Petviashvili equation, which models the nonlinear propagation of monomode wave packets exhibiting soliton solutions. The model serves as a mathematical depiction of wave characteristics and dynamics within specific physical systems. The main aim was to transform this nonlinear (3+1)-dimensional model into a second-order nonlinear ordinary differential equation through appropriate wave transformations. Our goal was to derive new, well-defined traveling wave solitons and periodic wave solutions. The results are presented in terms of exponential functions, hyperbolic trigonometric functions, and combinations of rational exponential functions with trigonometric and hyperbolic functions. These solutions reveal important features of the underlying physical phenomena and are original contributions. To fully understand the behavior of these solutions, we analyzed them through multiple graphical representations across various dimensions. Using software packages, we have thoroughly checked the validity of all the solutions we found by plugging each one into its own equation and finding that it was correct.