Revealing the Diversity of Travelling Wave Solutions in the Context of the Integrable Reduced Spin Hirota-Maxwell-Bloch Model Arising in Erbium-Doped Fibers

• Autores: Rashid Ali, Mujahid Iqba, Ahmed S. Hendy
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 3, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This study presents a theoretical and dynamical analysis of the coupled system of the integrable reduced spin Hirota-Maxwell-Bloch model, which outlines the femtosecond pulses that travel through an erbium-doped fiber. To this purpose, the travelling wave solutions of the reduced spin Hirota-Maxwell-Bloch model are examined using three novel ansatz: the Tanh-Coth approach, the Tan-Cot technique, and the Riccati modified extended simple equation method. As a result, numerous travelling wave structures, including singular travelling waves, rogue waves with periodic background, and other soliton types such as dark, bright, periodic, double periodic, and internal envelope solitons, are provided by these transformation-based methods under some determined constraint conditions. By contrasting our discovered wave solutions with existing literature, we demonstrate their uniqueness and their substantial contribution to the field of study. The fundamental mechanism of the model is further demonstrated through the incorporation of 3D models and contour plots to visualize some of the discovered solutions. The work is novel and significant since it additionally comprises several theorems pertaining to the existence of travelling waves, particularly solitary and soliton solutions, their classification, and extension. The resulting solutions and their physical structure, which replicate the dynamical characteristics of the moving wave distortion front created in the dispersive medium, provide a framework for the travelling wave phenomena.

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