Exact dynamical behavior for a dual Kaup–Boussinesq system by symmetry reduction and coupled trial equations method

Abstract

Abstract We propose a coupled trial equation method for a coupled differential equations system. Furthermore, according to the invariant property under the translation, we give the symmetry reduction of a dual Kaup–Boussinesq system, and then we use the proposed trial equation method to construct its exact solutions which describe its dynamical behavior. In particular, we get a cosine function solution with a constant propagation velocity, which shows an important periodic behavior of the system.

Keywords

• Trial equation method
• Symmetry
• The complete discrimination system for polynomial
• Exact solution
• Kaup–Boussinesq system