The (2+1)-dimensional Boussinesq equation plays an important role in mathematical physics. In this paper, we investigate some exact solutions of the (2+1)-dimensional variable-coefficient Boussinesq equation. Firstly, the Painlevé analysis is carried out, and an auto-Bäcklund transformation is constructed by means of a truncated Painlevé expansion combined with symbolic computation. Then, a class of new soliton-type solutions is derived. By selecting appropriate parameter values, detailed simulations are presented to illustrate the dynamical behavior of water wave propagation. Finally, the Lie point symmetries of the equation are studied, and several similarity reductions are derived by solving the corresponding characteristic equations.
J et al. (Mon,) studied this question.