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arXiv · 2601.13611

Quasi-periodic Dynamics for Multi-dimensional Quasi-linear Schr\"{o}dinger Equations via Resonant Mode Control

Zuhong You·Xiaoping Yuan
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Abstract

This paper focuses on the problem of quasi-periodic solutions for multi-dimensional quasi-linear Schr\"odinger 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.

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Zuhong You, Xiaoping Yuan. 2026-01-20. Quasi-periodic Dynamics for Multi-dimensional Quasi-linear Schr\"{o}dinger Equations via Resonant Mode Control. https://arxiv.org/abs/2601.13611

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