The Maxwell-Bloch equation and correlation functions for the penetrable Bose gas

We consider the quantum nonlinear Schrödinger equation in one space and one time dimension. We are interested in the non-free-fermionic case. We consider static temperature-dependent correlation functions. The determinant representation for the correlation functions simplifies in the small-mass limit of the Bose particle. In this limit we describe the correlation functions by the vacuum expectation value of a boson-valued solution for Maxwell-Bloch differential equation. We evaluate long-distance asymptotics of the correlation functions in the small-mass limit.