Coherent structures and statistical equilibrium states in a model of dispersive wave turbulence (Q2754439)

This is a brief review of results obtained for statistical description of the long-time evolution of a complex field governed by a nonintegrable version of the nonlinear Schrödinger equation in a finite-length one-dimensional model. A main idea, suggested by numerical observations, is that the field evolves to a state consisting of a single large-amplitude soliton, which concentrates almost all the initial energy of the field, and small-amplitude residual radiation waves around the soliton. It is demonstrated that a hypothesis postulating the microcanonical distribution for the density of radiation states, which, as usual, can be eventually reduced to the Boltzmann distribution, is in good agreement with results of systematical numerical simulations of different versions of the model.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00018].