Discrete Bound States in a Toy Model for Weak Turbulence and Implications for the Invariant Measure
Classical Analysis and ODEs
2025-10-28 v1 Analysis of PDEs
Abstract
A model Hamiltonian dynamical system has been derived to study frequency cascades in the cubic defocusing nonlinear Schr\"odinger equation on the torus. Here, we explore the framework for exploring a canonical ensemble formulation of the dynamics through classification of energy minimizers for fixed mass and characterizing the invariant measure in a neighborhood of those minimizers.
Keywords
Cite
@article{arxiv.2510.22090,
title = {Discrete Bound States in a Toy Model for Weak Turbulence and Implications for the Invariant Measure},
author = {Jeremy L. Marzuola and Jonathan C. Mattingly},
journal= {arXiv preprint arXiv:2510.22090},
year = {2025}
}
Comments
42 pages, 3 figures, comments welcome!!