Focusing mKdV equation: Two-phase solutions and their stability analysis
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909844019085312 |
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| author | Ling, Liming Sun, Xuan |
| author_facet | Ling, Liming Sun, Xuan |
| contents | In this work, we primarily focus on the two-phase solutions and their stability to the focusing mKdV equation. By employing the algebro-geometric approach in combination with an effective integration method, we construct explicit two-phase solutions and their corresponding wave-functions expressed in terms of the Riemann theta function. The spectral stability of two-phase solutions is examined via a modified squared-eigenfunction approach, and their stability with respect to subharmonic perturbations is further analyzed under spectrally unstable conditions. In addition, the orbital stability of the two-phase solutions is investigated. To the best of our knowledge, this study provides the first rigorous stability theory for the two-phase solutions of the focusing mKdV equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_12073 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Focusing mKdV equation: Two-phase solutions and their stability analysis Ling, Liming Sun, Xuan Exactly Solvable and Integrable Systems Mathematical Physics Analysis of PDEs In this work, we primarily focus on the two-phase solutions and their stability to the focusing mKdV equation. By employing the algebro-geometric approach in combination with an effective integration method, we construct explicit two-phase solutions and their corresponding wave-functions expressed in terms of the Riemann theta function. The spectral stability of two-phase solutions is examined via a modified squared-eigenfunction approach, and their stability with respect to subharmonic perturbations is further analyzed under spectrally unstable conditions. In addition, the orbital stability of the two-phase solutions is investigated. To the best of our knowledge, this study provides the first rigorous stability theory for the two-phase solutions of the focusing mKdV equation. |
| title | Focusing mKdV equation: Two-phase solutions and their stability analysis |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2510.12073 |