On the determining equations for the nonclassical reductions of the heat and Burgers’ equation

The determining equations for the nonclassical reductions of the heat and Burgers’ equations are considered. It is shown that both systems belong to a Burgers’ equation hierarchy. Each system is written in terms of the same matrix Burgers’ equation that is linearized via a matrix Hopf–Cole transformation. In essence, it is shown that both systems can be solved simultaneously. Their respective solutions are then presented in a very compact form.  2002 Elsevier Science (USA). All rights reserved.