A computational procedure for exact solutions of Burgers’ hierarchy of nonlinear partial differential equations

Abstract

This paper considers the exact solution of Burgers’ hierarchy of nonlinear evolution equations. We construct the general nth conservation law of the hierarchy and prove that these expressions may be transformed into ordinary differential equations. In particular, a coordinate transformation leads to the systematic reduction of the conservation law properties of the Burgers’ hierarchy. Such an approach yields a nonlinear equation, where a second transformation is derived to linearize the expression. Consequently, this approach describes a procedure for finding the exact solutions of the hierarchy. A formula of the nth solution is provided, and to demonstrate its application, we discuss the solution to several members of the nonlinear hierarchy.