On discrete rarefaction waves in a nonlinear Schr\"odinger equation toy model for weak turbulence
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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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