Breather-to-soliton transitions and nonlinear wave interactions for the higher-order generalized Gerdjikov-Ivanov equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909734246809600 |
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| author | Wang, Yanan Zhang, Minghe |
| author_facet | Wang, Yanan Zhang, Minghe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23067 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Breather-to-soliton transitions and nonlinear wave interactions for the higher-order generalized Gerdjikov-Ivanov equation Wang, Yanan Zhang, Minghe Pattern Formation and Solitons Mathematical Physics Exactly Solvable and Integrable Systems 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. |
| title | Breather-to-soliton transitions and nonlinear wave interactions for the higher-order generalized Gerdjikov-Ivanov equation |
| topic | Pattern Formation and Solitons Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2506.23067 |