BIFURCATIONS AND TRAVELING WAVE SOLUTIONS OF THE SPACE-TIME FRACTIONAL COUPLED BOUSSINESQ EQUATIONS

This paper mainly applies bifurcation theory to study the space-time fractional coupled Boussinesq equations. First, the space-time fractional differential equations with [Formula: see text]-truncated derivative are transformed into an ordinary differential equation. Then, the phase portraits of the equation are plotted. Based on the orbits of the phase portraits, different traveling wave solutions are established, including solitary wave solutions, periodic solutions, and singular solutions. Finally, the physical structures of some solutions are plotted with appropriate parameter values. The results show that the novelty of this paper lies in the combination of qualitative theory and quantitative calculation, which makes the paper more comprehensive and systematic. It fills the gaps in the model and yields many new exact traveling wave solutions of the space-time fractional coupled Boussinesq equations that differ from those previously discovered.