A toy model for frequency cascade in the nonlinear Schrodinger equation

2025/06/18 by Rémi Carles, Erwan Faou, Carles, Rémi +1
Computer Science · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2506.15226

openalex publication_date 2025/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an elementary approach to observe frequency cascade on forced nonlinear Schrödinger equations. The forcing term (which may also appear as a potential term instead) consists of a constant term, perturbed by a modulated Gaussian well. Algebraic computations provide an explicit frequency cascade when time and space derivatives are discarded from the nonlinear Schrödinger equation. We provide stability results, showing that when derivatives are incorporated in the model, the initial algebraic solution may be little affected, possibly over long time intervals. Numerical simulations are provided, which support the analysis.

Citations

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