COMPLETELY INTEGRABLE EQUATION FOR THE QUANTUM CORRELATION-FUNCTION OF NONLINEAR SCHRODINGER-EQUATION

Correlation functions of exactly solvable models can be described by d ifferential equations [1]. In this paper we show that for the non-free fermionic case, differential equations should be replaced by integro- differential equations. We derive an integrodifferential equation, whi ch describes a time and temperature dependent correlation function [ps i(0, 0)psi(dagger)(x, t)](T) of the penetrable Bose gas. The integro-d ifferential equation turns out to be the continuum generalization of t he classical nonlinear Schrodinger equation.