A MATRIX MODEL FOR THE CLASSICAL NONLINEAR SCHRÖDINGER EQUATION

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).