A study of the shallow water waves with some Boussinesq-type equations
Yue Kai, Shuangqing Chen, Kai Zhang, Zhixiang Yin
Abstract
In this paper, analytic solutions and dynamic properties of a variety of Boussinesq-type equations are established via the complete discrimination system for polynomial method. All the existing single traveling wave solutions to these equations as well as some new solutions are shown, and the Hamiltonian and topological properties to these equations are also presented. Considering the significance of the Boussinesq-type equations, our results would have wide applications in ocean engineering and fluid mechanics, like describing and predicting the solitary and periodic waves in various shallow water models.
Topics & Concepts
Boussinesq approximation (buoyancy)Shallow water equationsWaves and shallow waterType (biology)MathematicsKondratiev waveMathematical analysisGeophysical fluid dynamicsPhysicsMechanicsGeologyPaleontologyRayleigh numberConvectionThermodynamicsNatural convectionNonlinear Waves and SolitonsOcean Waves and Remote SensingCoastal and Marine Dynamics