Quasi-periodic Dynamics for Multi-dimensional Quasi-linear Schrödinger Equations via Resonant Mode Control
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912834270527488 |
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| author | You, Zuhong Yuan, Xiaoping |
| author_facet | You, Zuhong Yuan, Xiaoping |
| contents | This paper focuses on the problem of quasi-periodic solutions for multi-dimensional quasi-linear Schrödinger equation. To address the challenge of unbounded perturbations caused by quasi-linear terms in the equation, we define the resonant mode set $\mathcal{K}$ to control nonlinear resonant effects. Combining KAM (Kolmogorov-Arnold-Moser) ( or Nash-Moser ) theory and Fourier analysis methods, we prove that there are plenty of quasi-periodic solutions of the equation. We also present the Fourier expansion form of the solutions and the estimation of frequency shifts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13611 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasi-periodic Dynamics for Multi-dimensional Quasi-linear Schrödinger Equations via Resonant Mode Control You, Zuhong Yuan, Xiaoping Dynamical Systems This paper focuses on the problem of quasi-periodic solutions for multi-dimensional quasi-linear Schrödinger equation. To address the challenge of unbounded perturbations caused by quasi-linear terms in the equation, we define the resonant mode set $\mathcal{K}$ to control nonlinear resonant effects. Combining KAM (Kolmogorov-Arnold-Moser) ( or Nash-Moser ) theory and Fourier analysis methods, we prove that there are plenty of quasi-periodic solutions of the equation. We also present the Fourier expansion form of the solutions and the estimation of frequency shifts. |
| title | Quasi-periodic Dynamics for Multi-dimensional Quasi-linear Schrödinger Equations via Resonant Mode Control |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2601.13611 |