THE RIEMANN-HILBERT PROBLEM ASSOCIATED WITH THE QUANTUM NONLINEAR SCHRODINGER-EQUATION

We consider the dynamical correlation functions of the quantum nonline ar Schrodinger equation. In a previous paper we found that the dynamic al correlation functions can be described by the vacuum expectation va lue of an operator-valued Fredholm determinant. In this paper we show that a Riemann-Hilbert problem can be associated with this Fredholm de terminant. This Riemann-Hilbert problem formulation permits us to writ e down completely integrable equations for the Fredholm determinant an d to perform an asymptotic analysis for the correlation function.