Auto-Bäcklund transformation and similarity reductions to the variable coefficients variant Boussinesq system

Based on the closed connections among the homogeneous balance (HB) method, Weiss-Tabor-Carneval (WTC) method and Clarkson-Kruskal (CK) method, we study Bäcklund transformation and similarity reductions of the variable coefficients variant Boussinesq system. In the meantime, new exact solutions also are found.