On the method of preliminary group classification applied to the nonlinear heat equation ut=f(x,ux)uxx+g(x,ux)

Abstract

We apply the method of preliminary group classification to a specific class of the nonlinear heat equation, ie, . This results in an optimal system of one‐dimensional subalgebras, which will be used to find specific forms of the equation, which admit more symmetries and so allow us to find additional group invariant solutions. We extend this work by determining the potential symmetries of a closely related system, which gives rise to many new, additional solutions of the original equation.