The purpose of the paper is to consider an equivalence problem of second order partial differential equations for one unknown function of two independent variables under scale transformations. For this equivalence problem, explicit forms of invariant functions are given. In particular, if all of these invariant functions vanish, then PDEs are equivalent to the flat equation.
"Equivalence problem of second order PDE for scale transformations." Hokkaido Math. J. 40 (3) 313 - 335, October 2011. https://doi.org/10.14492/hokmj/1319595858