Classical Integrability in the Kipnis-Marchioro-Presutti model

We evaluate the full statistics of non-stationary heat transfer in the one-dimensional Kipnis-Marchioro-Presutti lattice gas model at long times by exploiting complete integrability of the equations of the macroscopic  fluctuation theory for this model. These equations are closely related to the derivative nonlinear Schroedinger equation (DNLS), and we solve them by the Zakharov-Shabat inverse scattering method (ISM) adapted by Kaup and Newell (1978) for the DNLS.