Long time behavior of solutions of nonlinear classical field equations: The example of NLS defocusing
Nonlinear and nonintegrable classical fields cannot relax for long times toward an ill defined thermal equilibrium. The specific example considered here is the long time dynamics of solutions of the nonlinear Schrödinger equation, in the defocusing case. I show, under some assumptions, that for long times a cascade of energy toward smaller and smaller scales introduces a kind of dissipation in a system that is formally reversible, and I give the scaling laws for this. Besides this relaxation by weak interaction between phonons, there is also a relaxation of localized vortical structures emitting phonons.
scientific article; zbMATH DE number 493564