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<p>In the present research, we explored soliton and various solitary wave solutions of the nonlinear complex Myrzakulov–Lakshmanan system by applying the extended simple equation method. For the first time, new types of soliton solutions are examined in different physical structures. The obtained results, expressed in trigonometric and exponential functional forms, reveal diverse soliton structures such as periodic solitons, peakon solitons, dark solitons, bright solitons, kink wave solitons, mixed dark–bright solitons, mixed kink and anti–kink wave optical solitons, combined solitary wave structures, and anti–kink wave solitons. Graphical representations of the solutions are provided through two–dimensional, contour, and three–dimensional plots using symbolic computation, demonstrating their physical significance. These newly developed solutions have potential applications in engineering, physics, nonlinear optics, optical fibers, laser optics, and other branches of nonlinear science. The proposed study highlights that the employed method is effective, efficient, easy to use, and powerful for obtaining exact solutions of nonlinear models.</p>

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Nonlinear Behavior of Dispersive Soliton and Solitary Wave Solutions of the Nonlinear Complex Myrzakulov–Lakshmanan System with Diverse Physical Structures

  • 期刊论文

  • 发表日期：

    2026年2月13日

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  • Mujahid Iqbal,
  • Jianqiao Liu,
  • Aly R. Seadawy,
  • Abeer Aljohani,
  • Ghadah Alhawael,
  • Ahmet Bekir

摘要

In the present research, we explored soliton and various solitary wave solutions of the nonlinear complex Myrzakulov–Lakshmanan system by applying the extended simple equation method. For the first time, new types of soliton solutions are examined in different physical structures. The obtained results, expressed in trigonometric and exponential functional forms, reveal diverse soliton structures such as periodic solitons, peakon solitons, dark solitons, bright solitons, kink wave solitons, mixed dark–bright solitons, mixed kink and anti–kink wave optical solitons, combined solitary wave structures, and anti–kink wave solitons. Graphical representations of the solutions are provided through two–dimensional, contour, and three–dimensional plots using symbolic computation, demonstrating their physical significance. These newly developed solutions have potential applications in engineering, physics, nonlinear optics, optical fibers, laser optics, and other branches of nonlinear science. The proposed study highlights that the employed method is effective, efficient, easy to use, and powerful for obtaining exact solutions of nonlinear models.