On construction of mappings relating partial differential equations

Abstract

Mapping partial differential equations into other partial differential equations has been a useful tool in finding solutions. One such example is the Hopf-Cole transformation which maps the linear heat equation into the Burgers equation. So that solutions of the linear heat equation can be used to generate solutions of the Burgers equation. We study such mappings between a (2+1) variable coefficients heat equation and the linear heat equation with constant coefficients through the symmetry analysis.