Completely Integrable Equation for the Quantum Correlation Function of Nonlinear Schrödinger Eqaution
T. Kojima, V. Korepin, N. Slavnov
Abstract
Correlation functions of exactly solvable models can be described by differential equation [Barough, McCoy, Wu]. 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 <ψ(0,0)ψ(x,t)>T of penetrable Bose gas. The integro-differential equation turns out be the continuum generalization of classical nonlinear Schrödinger equation.
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