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Korepin V. E., Slavnov N. A.
The Riemann-Hilbert problem associated with the quantum Nonlinear
ABSTRACT. We consider the dynamical correlation functions
of the quantum Nonlinear Schrodinger equation. In a previous paper
we found that the dynamical correlation functions can be described by
the vacuum expectation value of an operator-valued Fredholm
determinant. In this paper we show that a Riemann--Hilbert problem
can be associated with this Fredholm determinant. This
Riemann--Hilbert problem formulation permits us to write down
completely integrable equations for the Fredholm determinant and to
perform an asymptotic analysis for the correlation function.