96-689 T. Kojima, V.E. Korepin and N.A. Slavnov

Completely Integrable Equation for the Quantum Correlation Function of Nonlinear Schr\"odinger Eqaution. (52K, LaTeX) Dec 30, 96

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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.

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