Optimal systems, similarity reductions and new conservation laws for the classical Boussinesq–Burgers system

The classical Boussinesq–Burgers (CBB) system is investigated by applying the Lie symmetry analysis method. On the one hand, when Lie point symmetries of this system are studied, the optimal system of one-dimensional subalgebras can also be obtained by using Ibragimov’s method. On the other hand, the similarity reductions and the invariant solutions are discussed based on the optimal system. Furthermore, the conservation laws of the CBB system are constructed through a new conservation theorem.