A MATRIX MODEL FOR THE CLASSICAL NONLINEAR SCHRÖDINGER EQUATION

Abstract

The effective scalar theory is constructed for the nonlinear Schrödinger (NS) matrix equation, which gives us the tool for investigating the two-point correlator and the partition function for some (classical) NS-like systems. The spatial dependence of the correlator coincides with the free correlator in all quantization schemes. For the classical NS system the effective two-matrix model is found (throughout this paper both the model with compactified space variables x ∈ S1 and the model corresponding to noncompactified x ∈ ℝ are implied).