- In this paper, we give a classification for mappings of the form ƒ(x,y)=(x+u(p(x,y)),y+v(q(x,y))), u,v∈C[t], p,q∈C[x,y] , i.e., mappings with a composite part, that satisfy the Jacobian hypothesis. This is done for those mappings for which a certain “no cancellation” argument can be applied. The proof is rather technical, and strangely it relies on the study of the rational solutions of the socalled Burger's equation with no viscosity. This is a nonlinear scalar hyperbolic PDE that modelizes the behavior of gas with no viscosity. Originally, it served for street traffic model.