Solutions to Space-Time Fractional Complex Ginzburg-Landau Equations With the Complete Discrimination System for Polynomial Method

Abstract

The space-time fractional complex Ginzburg-Landau equation was studied. Firstly, the space-time fractional complex Ginzburg-Landau equation was transformed into the ordinary differential equation through the fractional complex transform. Secondly, the ordinary differential equation was reduced to an elementary integral form. Finally, a series of exact solutions including solitary wave solutions, rational function type solutions, triangle function type periodic solutions, and Jacobian elliptic function doubly-periodic solutions, were constructed with the complete discrimination system for polynomial method.