Symmetry and Integrability of PT -Symmetric Semi-discrete Short pulse equation: A study of Rogue, Breather, and Soliton Solutions

• Asifa Ashraf ^[1] ; Zeeshan Amjad ^[1] ; Wen-Xiu Ma ^[2] ; Nauman Raza ^[3]
  1. [1] Zhejiang Normal University

     Zhejiang Normal University

     China

     
  2. [2] North-West University, University of South Florida, Zhejiang Normal University, King Abdulaziz University
  3. [3] University of the Punjab, Near East University

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 5, 2025
• Idioma: inglés
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• Resumen

  • Spontaneous symmetry breaking and PT -symmetry attracts the modern researcher due to its implementation in many fields such as microwave propagation, nonlinear optics. This article studies the PT -symmetric semi-discrete short pulse equation (PT -sdSPE) that can be viewed as a cognate to the Ablowitz-Ladik lattice in the ultra-short-pulse regime. The Lax pair of the system is constructed and demonstrated that one can obtain a variety of new integrable models by symmetry reductions. Furthermore, quasi-grammian solutions of PT -sdSPE are presented using the binary Darboux transformation. Finally, as an explicit example, symmetry preserving and non-preserving grammians, rogue, breather and soliton solutions are celebrated.

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