Behavior of a Model Dynamical System with Applications to Weak Turbulence

J. Colliander, Jeremy L. Marzuola, Tadahiro Oh, Gideon Simpson

Type: Article

Publication Date: 2013-01-01

Citations: 0

DOI: https://doi.org/10.17615/qywb-ae73

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.

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arXiv (Cornell University) - View - PDF
Edinburgh Research Explorer (University of Edinburgh) - View - PDF
Carolina Digital Repository (University of North Carolina at Chapel Hill) - View - PDF

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