A class of constant coefficient nonlinear equations that are solvable by the heat kernel

Abstract

In this paper, we document a new tractable method to solve nonlinear classes of partial differential equations subject to initial-values. The method involves a detailed transformation procedure, underpinned by the Lie pint symmetries of the one dimensional heat transfer equation. We illustrate the approach with the famous Burgers’ equation, Potential Burgers’ equation and the Hamilton-Jacobi-Bellman equation. This approach identifies new solutions of these nonlinear equations, which enhances our comprehension of its analytical properties and solution behaviour.