On the irreducible part of the current correlation function in quantum completely integrable models

A method for finding irreducible parts of currents correlation function in completely integrable quantum models with the $R$-matrix of the XXX-type is suggested. Explicit formulas for the Fouries coefficients of the irreducible part $A_n^k$ are obtained for $n=4,5$ and some general properties of this coefficients for arbitrary $n$ are pointed out. It is found that in the quantum nonlinear Schrödinger equation (in the repulsion case at finite density) the expansion of the currents correlator in the power series in the inverse large coupling constant agrees (at least up to the second order) with the hypothesis about the power law of the decreasing of the amplitude of correlator oscillations at large distances.