Modulational instability, rogue waves and multi-pole solitons for the fifth-order reverse space-time nonlinear Schrödinger equation

This study presents a systematic investigation of modulational instability and nonlinear wave dynamics in the reverse space-time fifth-order nonlinear Schrödinger equation. Particular focus is given to rogue wave generation and multi-pole soliton interactions. The modulational instability analysis predicts the emergence of rogue waves and rogue wave-rational soliton transitions in the focusing regime. Higher-order rogue wave solutions are constructed through generalized Darboux transformation. Notably, we introduce energy spectrum to investigate the dynamic behaviors of rogue waves. Furthermore, we derive multi-pole soliton solutions and rigorously establish their asymptotic decomposition into weakly interacting fundamental solitons. The results significantly advance the understanding of nonlinear waves in high-order nonlocal integrable systems.