Abstract
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.