Bifurcations and exact traveling wave solutions of the Khorbatly's geophysical Boussinesq system

For a geophysical Boussinesq system, the corresponding traveling wave system is a planar dynamical system with a singular straight line. In this paper, by using the techniques from dynamical systems and singular traveling wave theory developed by Li and Chen [10], we analyze the corresponding dynamical system and find the bifurcations of phase portraits. The dynamical behaviors can also be derived. Under a given parameter condition, exact explicit solitary wave solutions and periodic wave solutions can be found.