The aim of this work is to study the equilibrium properties of the Tzitz ́eica-Bullogh-Dodd (TBD) model, a classical integrable field theory. Computing observables’ averages for a Generalized Gibbs Ensable is a very challenging task but there exists a method that allows to do so in the case of the Sinh-Gordon model. I will develop the tools necessary to adapt this technique to the model of interest. The focus will mainly be on the numerical tools necessary for the time evolution and the transfer matrix computation and on the inverse scattering method for the TBD model.