Exact solutions and bifurcations of the time-fractional coupled Boussinesq-Burgers equation

Abstract

In this paper, the time-fractional coupled Boussinesq-Burgers equations are studied to construct exact solutions by utilizing the modified extended tanh-function method, the improved (G'/G) method, the two variables (G'/G,1/G)-expansion method and bifurcation analysis. Firstly, based on the modified Riemann-Liouville derivative and traveling wave transformation, the equations are rewritten as an ordinary differential equation. Some exact solutions, including singular, periodic, kink, anti-kink, soliton and periodic-singular solutions, are derived. Then, we graphically describe the 3D, density plots and solution profiles of some solutions by setting suitable parameters. Finally, the effectiveness of the methods applied is verified via bifurcation theory.