  Correlation functions of exactly solvable models can be described by
differential equation [Barough, McCoy, Wu]. In this paper we show that for non
free fermionic case differential equations should be replaced by
integro-differential equations.
  We derive an integro-differential equation, which describes time and
temperature dependent correlation function $<\psi(0,0)\psi^\dagger(x,t)>_T$ of
penetrable Bose gas. The integro-differential equation turns out be the
continuum generalization of classical nonlinear Schr\"odinger equation.

High Energy Physics - Theory;Condensed Matter;Quantum Algebra;Exactly Solvable and Integrable Systems;Quantum Algebra;Exactly Solvable and Integrable Systems