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

Asifa Ashraf, Zeeshan Amjad, Wen Xiu Ma, Nauman Raza

• 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.