On discrete rarefaction waves in a nonlinear Schr\"odinger equation toy model for weak turbulence
Sebastian Herr, Jeremy L. Marzuola
TL;DR
This paper investigates discrete rarefaction wave solutions within a simplified nonlinear Schrödinger model to better understand frequency cascades and weak turbulence phenomena.
Contribution
It extends previous work by analyzing rarefaction wave-like solutions in a toy model for weak turbulence in the nonlinear Schrödinger equation.
Findings
Identification of rarefaction wave solutions in the toy model
Insights into frequency cascade mechanisms
Enhanced understanding of weak turbulence dynamics
Abstract
We explore further the rarefaction wave-like solutions recently discussed in work of the second author with J. Colliander, T. Oh and G. Simpson for a model Hamiltonian dynamical system derived by Colliander-Keel-Staffilani-Takaoka-Tao to study frequency cascades in the cubic defocusing nonlinear Schr\"odinger equation on the torus.
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