T. Kojima, V.E. Korepin and N.A. Slavnov
Completely Integrable Equation for the
Quantum Correlation Function of Nonlinear Schr\"odinger Eqaution.
(52K, LaTeX)
ABSTRACT. Correlation functions of exactly solvable models can be described by
differential equations [Barough E., McCoy B.M. and Wu T.T.,
Phys. Rev. Lett. {\bf 31} (1973) 1409.]. In this paper we show that for
non free fermionic case differential equations should be replaced by
integro-differential equations. We derive an integro-differential
equation, which describes time and temperature dependent correlation
function $\langle\psi(0,0)\psi^\dagger(x,t)\rangle_T$ of penetrable
Bose gas. The integro-differential equation turns out be the continuum
generalization of classical nonlinear Schr\"odinger equation.