Variants of the two-dimensional boussinesq equation with compactons, solitons, and periodic solutions

Variants of the two-dimensional Boussinesq equation with positive and negative exponents are studied. The sine-cosine ansatz is fruitfully used to carry out the analysis. Exact solutions of different physical structures: compactons, solitary patterns, solitons, and periodic solutions, are obtained. The quantitative change in the physical structure of the solutions is shown to depend mainly on the exponent of the wave function u(x, t) and on the ratio a/b of the derivatives of u(x, t).