Abstract
We experimentally explore solutions to a model Hamiltonian dynamical system recently derived to study frequency cascades in the cubic defocusing nonlinear Schrödinger 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 and periodic solutions in an associated problem, and find experimental evidence of hyperbolic behavior. Many of our results rely on reframing the dynamical system using a hydrodynamic formulation.
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