Abstract
Variants of the two-dimensional Boussinesq-type equations with positive and negative exponents are studied. The bifurcation theory of dynamic systems is fruitfully used to carry out the analysis. The dynamical behavior of different physical structure: solitary patterns, solitons, kink, breaking and periodic wave solutions, is obtained. The quantitative change in the physical structure of the solutions is shown to depend on the systemic parameters. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.
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