This paper uses Lie symmetry group methods to study PDEs of the form ut = xuxx + f (x)ux. We show that when the drift function f is a solution of a family of Ricatti equations, then symmetry techniques can be used to find a fundamental solution. © 2004 Elsevier Inc. All rights reserved.
Craddock, M., & Platen, E. (2004). Symmetry group methods for fundamental solutions. Journal of Differential Equations, 207(2), 285–302. https://doi.org/10.1016/j.jde.2004.07.026