Breather-to-soliton transitions and nonlinear wave interactions for the higher-order generalized Gerdjikov-Ivanov equation

TL;DR

This paper explores complex wave transformations and interactions in a higher-order integrable system, revealing new wave types and transition conditions through analytical solutions and asymptotic analysis.

Contribution

It introduces novel nonlinear wave solutions and detailed transition conditions for the higher-order generalized Gerdjikov-Ivanov equation, advancing understanding of wave metamorphosis.

Findings

Identified conditions for breather-to-soliton transitions

Discovered new nonlinear wave structures like W-shaped and M-shaped solitons

Analyzed interactions among various nonlinear waves

Abstract

In this paper, we systematically investigate the intricate dynamics of the breather-to-soliton transitions and nonlinear wave interactions for the higher-order generalized Gerdjikov-Ivanov equation. The transition conditions of the breather-to-soliton are established and the novel nonlinear converted waves, including the W-shaped soliton, M-shaped soliton, multi-peak soliton, anti-dark soliton and periodic wave solution are discussed. Meanwhile, the interactions among the above nonlinear converted waves are explored by choosing appropriate parameters. Furthermore, we derive the double-pole solutions exhibiting breather-to-soliton transitions and employ the asymptotic analysis method to analyze the dynamics of the asymptotic solitons for the double-pole anti-dark soliton. This work deepens the fundamental understanding of nonlinear wave metamorphosis induced by higher-order terms in integrable systems.