Breather-to-soliton transitions and nonlinear wave interactions for the higher-order modified Gerdjikov-Ivanov equation (2506.23067v1)

Abstract: In this paper, we systematically investigate the intricate dynamics of the breather-to-soliton transitions and nonlinear wave interactions for the higher-order modified Gerdjikov-Ivanov equation. We discuss the transition conditions of the breather-to-soliton and obtain different types of nonlinear converted waves, including the W-shaped soliton, M-shaped soliton, multi-peak soliton, anti-dark soliton and periodic wave solution. Meanwhile, the interactions among the above nonlinear converted waves are explored by choosing appropriate parameters. Furthermore, we derive the double-pole breather-to-soliton transitions and apply the asymptotic analysis method to analyze the dynamics of the asymptotic solitons for the double-pole anti-dark soliton.