Higher-dimensional integrable deformations of the classical Boussinesq–Burgers system*

In this paper, the (1+1)-dimensional classical Boussinesq–Burgers (CBB) system is extended to a (4+1)-dimensional CBB system by using its conservation laws and the deformation algorithm. The Lax integrability, symmetry integrability and a large number of reduced systems of the new higher-dimensional system are given. Meanwhile, for illustration, an exact solution of a (1+1)-dimensional reduced system is constructed from the viewpoint of Lie symmetry analysis and the power series method.