An extension of the direct method and similarity reductions of a generalized Burgers equation with an arbitrary derivative function

In this paper, we extend the well-known direct method proposed by Clarkson and Kruskal for finding similarity reductions of partial differential equations. It follows that some new similarity reductions of the generalized Burgers equation, such as travelling wave reduction, logarithmic reduction, power reduction, rational fractional reduction, etc, are derived, in which some of these cannot be obtained solely by using the direct method. The similarity reductions obtained are interpreted by the nonclassical symmetry Lie group.