Equivalence transformations of families of quasi-linear elliptic equations of the second order of a function of two variables

In this work, we search for infinitesimal equivalence transformations of 16 families of quasi-linear elliptic equations of the second order in two variables. A symmetry reduction has been performed for the families of equations u tt + u xx = f(t,x,u), u tt + u xx = f(x,u).