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We consider the dynamical correlation functions of the quantum NonlinearSchrodinger equation. In a previous paper we found that the dynamicalcorrelation functions can be described by the vacuum expectation value of anoperator-valued Fredholm determinant. In this paper we show that aRiemann-Hilbert problem can be associated with this Fredholm determinant. ThisRiemann-Hilbert problem formulation permits us to write down completelyintegrable equations for the Fredholm determinant and to perform an asymptoticanalysis for the correlation function.Comment: 21 pages, Latex, no figure

The Riemann - Hilbert problem associated with the quantum nonlinear Schrödinger equation