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arXiv · 2506.23067

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

Yanan Wang·Minghe Zhang
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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.

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Yanan Wang, Minghe Zhang. 2025-08-12. Breather-to-soliton transitions and nonlinear wave interactions for the higher-order generalized Gerdjikov-Ivanov equation. https://arxiv.org/abs/2506.23067

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