Gianni Jona-Lasinio and his collaborators have proposed in the early 2000’s a non-linear action functional that encodes the macroscopic fluctuations and the large deviations for a wide class of diffusive systems out of equilibrium, by generalizing a variational principle due to Kipnis, Olla and Varadhan. This theory, called the Macroscopic Fluctuation Theory (MFT) shows that large deviations far from equilibrium can be found by solving two coupled non-linear hydrodynamic equations. In this talk, we shall show that the MFT equations for the symmetric exclusion process are classically integrable and can be solved with the help of the inverse scattering method, originally developed to study solitons in dispersive non-linear wave equations (such as KdV or NLS).