Classical and quantum operator nonlinear schrodinger equation. I

Abstract

We consider generalizations of the classical nonlinear Schrödinger equation, iψ_t = ψ_xx + 2ψψ⁺ψ, to operator functions ψ=ψ(x,t) and their solvability via the inverse scattering method. This provides a new class of soluble field theories in one-space, one-time dimensions, which, after quantization, are equivalent to a system of many, nonidentical, particles with σ-function interactions and a spectrum of bound states richer than in the usual model.