On qualitative analysis to nonlinear coupled systems

In this paper, two nonlinear coupled systems, one is fractional-order with Riemann-Liouville (RL) derivative and another is integer-order, are considered via the bifurcation method and the complete discrimination system for polynomial method. Though our results, the necessity of qualitative analysis to nonlinear equations can be seen very clearly; the existences of periodic and a variety kinds of soliton solutions could be established even when the solution can not be given explicitly by the elementary functions nor commonly used special functions. Concrete examples are also carried out to illustrate our results.