Dispersionless limit of integrable models

Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these equations are integrable in the Hamiltonian sense and appear in the study of topological minimal models. In the first part of the review, we will give a brief introduction to integrable models, mainly its Lax representation. Then, we will introduce the dispersionless limit and show some of our results concerning the two-component hyperbolic system of equations such as the polytropic gas and Born-Infeld equations.