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We present a new method allowing us to derive the long-time andlarge-distance asymptotic behavior of the correlations functions of quantumintegrable models from their exact representations. Starting from the formfactor expansion of the correlation functions in finite volume, we explain howto reduce the complexity of the computation in the so-called interactingintegrable models to the one appearing in free fermion equivalent models. Weapply our method to the time-dependent zero-temperature current-currentcorrelation function in the non-linear Schr\"{o}dinger model and compute thefirst few terms in its asymptotic expansion. Our result goes beyond theconformal field theory based predictions: in the time-dependent case, othertypes of excitations than the ones on the Fermi surface contribute to theleading orders of the asymptotics.

Long-time and large-distance asymptotic behavior of the current-current correlators in the non-linear Schr\"{o}dinger model