Higher dimensional integrable deformations of the classical Boussinesq-Burgers system

Abstract

In this paper, (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 CBB system are given. What's more, for illustration, we study a (1+1)-dimensional reduced system of higher dimensional system and its exact solution is constructed by using Lie symmetry analysis and the power series method.