Authors:Fei Xu (Jilin University), Yong Li (Jilin University)
Abstract:We study the cubic weakly nonlinear Schrödinger equation with randomized spatially quasi-periodic initial data in higher dimensions. Under a polynomial decay assumption in Fourier space, we establish a \emph{Large Deviations Principle} for rogue waves in the so-called \emph{subcritical} time regime.
The proof proceeds in two main steps. We first characterize the distribution of the linear solution and establish the corresponding linear large deviations principle. The lower bound is obtained via pointwise estimates, while the upper bound follows from a combination of truncation and probabilistic arguments. {The method used in this step appears to be {\em new}; compare with \cite{GGKS23}.} We then perform a detailed combinatorial analysis of the Picard iteration, deriving an effective bound for the Duhamel term and thereby establishing the nonlinear large deviations principle.
From: Fei Xu [view email]
[v1]
Sun, 19 Apr 2026 04:37:26 UTC (30 KB)
[v2]
Sat, 13 Jun 2026 17:10:30 UTC (33 KB)
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