Well-posedness to nonlinear Schrödinger-Gerdjikov-Ivanon equation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917099854626816 |
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| author | Niu, Sucai Zhu, Junyi |
| author_facet | Niu, Sucai Zhu, Junyi |
| contents | The Riemann-Hilbert approach is extended to discuss the well-posedness of the nonlinear Schrödinger-Gerdjikov-Ivanon equation. The Lipschitz continuity of potential in $H^{2}(\mathbb{R})\cap H^{1,1}(\mathbb{R})$ to scattering data is obtained through direct scattering transform. Two Riemann-Hilbert problems are constructed, and two sets of the reflection coefficients, that is $r(k)$ and $r_\pm(z)$, are introduced. The Lipschitz continuity from the reflection coefficients $r_\pm(z)$ in $H^{1}(\mathbb{R})\cap L^{2,1}(\mathbb{R})$ to the potential is estimated via the potential reconstruction. Existence of global solutions of NLS-GI equation is considered by the Riemann-Hilbert problem without eigenvalues or resonances. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18228 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posedness to nonlinear Schrödinger-Gerdjikov-Ivanon equation Niu, Sucai Zhu, Junyi Analysis of PDEs Mathematical Physics The Riemann-Hilbert approach is extended to discuss the well-posedness of the nonlinear Schrödinger-Gerdjikov-Ivanon equation. The Lipschitz continuity of potential in $H^{2}(\mathbb{R})\cap H^{1,1}(\mathbb{R})$ to scattering data is obtained through direct scattering transform. Two Riemann-Hilbert problems are constructed, and two sets of the reflection coefficients, that is $r(k)$ and $r_\pm(z)$, are introduced. The Lipschitz continuity from the reflection coefficients $r_\pm(z)$ in $H^{1}(\mathbb{R})\cap L^{2,1}(\mathbb{R})$ to the potential is estimated via the potential reconstruction. Existence of global solutions of NLS-GI equation is considered by the Riemann-Hilbert problem without eigenvalues or resonances. |
| title | Well-posedness to nonlinear Schrödinger-Gerdjikov-Ivanon equation |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2511.18228 |