Kink wave, dark and bright soliton solutions for complex Ginzburg–Landau equation using Lie symmetry method

Abstract In this paper, using Lie symmetry method, some new soliton and doubly periodic solutions of the complex Ginzburg–Landau equation (CGLE) with two forms of nonlinearity are obtained. The obtained solutions are implicit solutions and explicit solutions in the form of Jacobi and Weierstrass elliptic functions. Under some conditions, we can retrieve kink wave, dark and bright soliton solutions for the CGLE from the obtained doubly periodic solutions.