Optical Solitons to the Ginzburg–Landau Equation Including the Parabolic Nonlinearity

The major goal of the present paper is to construct optical solitons of the Ginzburg–Landau (GL) equation including the parabolic nonlinearity. Such an ultimate goal is formally achieved with the aid of symbolic computation, a complex transformation, and Kudryashov and exponential methods. Several numerical simulations are given to explore the influence of the coefficients of nonlinear terms on the dynamical features of the obtained optical solitons. To the best of the authors’ knowledge, the results reported in the current study, classified as bright and kink solitons, are new and have been acquired for the first time.