Bifurcations and the Exact Solutions of the Time-Space Fractional Complex Ginzburg-Landau Equation with Parabolic Law Nonlinearity

This paper studies the bifurcations of exact solutions for time–space fractional complex Ginzburg–Landau equation with parabolic law nonlinearity. Interestingly, different parameters, there are kinds first integrals corresponding traveling wave systems. Using method dynamical systems, which is from previous works, we obtain phase portraits In addition, derive parametric representations solitary solutions, periodic kink and anti-kink peakon compacton under parameter conditions.