Second-order differential invariants of a family of diffusion equations

Abstract

The equivalence transformation algebra $L_{\\cal E}$ for the class of\nequations $u_t -u_{xx}=f(u, u_x) $ is obtained. After getting the differential\ninvariants with respect to $L_{\\cal E}$, some results which allow to linearize\na subclass of equations are showed. Equations like the standard deterministic\nKPZ equation fall in this subclass.\n