Allowed transformations and symmetry classes of variable coefficient Burgers equations

The allowed transformations and Lie point symmetries of variable coefficient Burgers (VCB) equations u 1 + f ( x , t ) uu x + g ( x , t ) u xx =0 which come from shock waves and sound waves are studied. The symmetry group is shown to be at most five-dimensional, and this occurs if and only if f ; and g can be transformed into constants. All VCB equations with one- to four-dimensional symmetry groups are identified.