ALLOWED TRANSFORMATIONS AND SYMMETRY CLASSES OF VARIABLE-COEFFICIENT BURGERS EQUATIONS

The allowed transformations and Lie point symmetries of variable coeff icient Burgers (VCB) equations u(t) + 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 w ith one- to four-dimensional symmetry groups are identified.