On the differential invariants of a family of diffusion equations

M. Torrisi; R. Tracinà

doi:10.1088/0305-4470/38/34/006

paper

On the differential invariants of a family of diffusion equations

arXiv:nlin/0402021 · doi:10.1088/0305-4470/38/34/006

Abstract

The equivalence transformation algebra $L_{E}$ for the class of equations $u_{t} - u_{xx} = f (u, u_{x})$ is obtained. After getting the differential invariants with respect to $L_{E}$ , some results which allow to linearize a subclass of equations are showed. Equations like the standard deterministic KPZ equation fall in this subclass.

15 pages