Initial boundary value problems for integrable systems: towards the long time asymptotics

Abstract

Abstract. The long time behavior of solutions of (Dirichlet) initial boundary value prob-lems for the focusing nonlinear Schrödinger equation in the case of (asymptotically) periodic boundary conditions of special (one-frequency) structure is considered both theoretically and numerically. The results of numerical simulations are shown to confirm the theoretical description in the parameter ranges where the assumption about the one-frequency character of the Neumann boundary values is (theoretically) admissible, whereas in the other ranges they suggest a more complicated description of the behavior of these values. 1.