Symmetries, travelling-wave and self-similar solutions of the Burgers hierarchy

We examine the general element of the Burgers Hierarchy, ut+∂∂x(∂∂x−u)nu=0,n=0,1,2,…, for its Lie point symmetries. We use these symmetries to construct traveling-wave and self-similar solutions. We observe that the general member of the hierarchy can be rendered as a linear (1+1)-evolution equation by means of an elementary Riccati transformation and examine this equation for its Lie point symmetries. With the use of these symmetries we can construct the traveling-wave and self-similar solutions in closed form.