Exact solutions and conservation laws of multi Kaup–Boussinesq system with fractional order

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.…”

Linear stability of exact solutions for the generalized Kaup-Boussinesq equation and their dynamical evolutions

“…which can also be degenerated into the periodic wave solution in form of trigonometric function for case of u 2 = u 3 , whose form is very similar to the trigonometric function in the infinite interval (−∞, u 4 ], which is Moreover, in the special case u 3 = u 4 the periodic wave solution (27) can degenerate into the solitary wave solution of the form…”

“…Dutykh and Ionescu-Kruse [10] found analytical multi-pulsed traveling wave solutions of the KB equation by means of the simple and geometrically intuitive phase space analysis. Recently, the exact solutions and conservation laws of multi KB system with fractional order are also considered [27].…”

“…Still there are some other degeneration cases for the periodic wave solution (27). For example, it degenerates into the trivial constant solution u = u 2 for u 1 = u 2 .…”