Scholarlink

<p>In this paper, we investigate exact analytical solutions of the (2+1)-dimensional complex modified Korteweg–de Vries (CmKdV) system using the truncated M-fractional derivative together with the Jacobi elliptic function expansion method. The CmKdV system plays a central role in modeling nonlinear wave propagation in optics, plasma physics, and fluid dynamics. By applying the truncated M-fractional derivative, the system is transformed into a more tractable form, enabling the effective use of the Jacobi elliptic function expansion method to construct exact soliton and periodic wave solutions. The results offer deeper insight into the system’s nonlinear dynamics and highlight the robustness of the proposed method. Graphical simulations generated in Mathematica illustrate the physical behavior of the obtained solutions across multiple dimensions, such as two-dimensional, three-dimensional, and contour, and the influence of time on the wave propagations. Overall, combining the Jacobi elliptic function expansion method and truncated M-fractional derivatives creates a strong framework for solving complex differential equations, leading to new possibilities. Opportunities for research and development exist. This research adds to our understanding of the (2+1)-dimensional complex modified Korteweg-de Vries (CmKdV) system and demonstrates how theoretical mathematics can be applied to real concerns. Mathematical modeling and computational visualization can significantly impact engineering and science, and our findings promote a multidisciplinary approach to research.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Optical soliton wave profiles for the (2 + 1)-dimensional complex modified Korteweg–de Vries system with the impact of fractional derivative via analytical approach

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年2月11日

查看全文
  • Muhammad Ishfaq Khan,
  • Meraj Ali Khan,
  • Mujahid Iqbal,
  • Weam Gaoud Alghabban,
  • Abeer Aljohani,
  • Ibrahim Al-Dayel,
  • Baboucarr Ceesay

摘要

In this paper, we investigate exact analytical solutions of the (2+1)-dimensional complex modified Korteweg–de Vries (CmKdV) system using the truncated M-fractional derivative together with the Jacobi elliptic function expansion method. The CmKdV system plays a central role in modeling nonlinear wave propagation in optics, plasma physics, and fluid dynamics. By applying the truncated M-fractional derivative, the system is transformed into a more tractable form, enabling the effective use of the Jacobi elliptic function expansion method to construct exact soliton and periodic wave solutions. The results offer deeper insight into the system’s nonlinear dynamics and highlight the robustness of the proposed method. Graphical simulations generated in Mathematica illustrate the physical behavior of the obtained solutions across multiple dimensions, such as two-dimensional, three-dimensional, and contour, and the influence of time on the wave propagations. Overall, combining the Jacobi elliptic function expansion method and truncated M-fractional derivatives creates a strong framework for solving complex differential equations, leading to new possibilities. Opportunities for research and development exist. This research adds to our understanding of the (2+1)-dimensional complex modified Korteweg-de Vries (CmKdV) system and demonstrates how theoretical mathematics can be applied to real concerns. Mathematical modeling and computational visualization can significantly impact engineering and science, and our findings promote a multidisciplinary approach to research.