Behavior of a Model Dynamical System with Applications to Weak Turbulence
Analysis of PDEs
2012-09-17 v2 Dynamical Systems
Abstract
We experimentally explore solutions to a model Hamiltonian dynamical system derived in Colliander et al., 2012, to study frequency cascades in the cubic defocusing nonlinear Schr\"odinger equation on the torus. Our results include a statistical analysis of the evolution of data with localized amplitudes and random phases, which supports the conjecture that energy cascades are a generic phenomenon. We also identify stationary solutions, periodic solutions in an associated problem and find experimental evidence of hyperbolic behavior. Many of our results rely upon reframing the dynamical system using a hydrodynamic formulation.
Cite
@article{arxiv.1209.0827,
title = {Behavior of a Model Dynamical System with Applications to Weak Turbulence},
author = {James E. Colliander and Jeremy L. Marzuola and Tadahiro Oh and Gideon Simpson},
journal= {arXiv preprint arXiv:1209.0827},
year = {2012}
}
Comments
22 pages, 14 figures