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

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.

Traveling Wave Solution of the Kaup–Boussinesq System with Beta Derivative Arising from Water Waves

“…For more than 40 years, the study of predecessors on the Kaup-Boussinesq system has covered a wide range of felds and made many achievements. Especially, the study of traveling wave solutions of the Kaup-Boussinesq system have become a very important research feld [1][2][3][4][5][6]. Many important methods are also used to construct traveling wave solutions [7][8][9][10][11][12] and optical soliton solutions [13][14][15][16][17] of the Kaup-Boussinesq system.…”