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arXiv · 2510.22090

Discrete Bound States in a Toy Model for Weak Turbulence and Implications for the Invariant Measure

Jeremy L. Marzuola·Jonathan C. Mattingly
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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.

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Jeremy L. Marzuola, Jonathan C. Mattingly. 2025-10-25. Discrete Bound States in a Toy Model for Weak Turbulence and Implications for the Invariant Measure. https://arxiv.org/abs/2510.22090

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