Pseudo-spectral approach for extracting optical solitons of the complex Ginzburg Landau equation with six nonlinearity forms

In this paper, a compelling pseudo-spectral approach namely split-step Fourier transform (SSFT) is utilized for the first time to report the complex Ginzburg Landau (CGL) equation. In this regard, six nonlinear forms of this notable equation are associated with this model, which are the kerr law nonlinearity, power law nonlinearity, quadratic-cubic nonlinearity, cubic-quintic nonlinearity, dual power nonlinearity, and polynomial law nonlinearity. Since opting for an analytical solution is complicated and only provided for a limited set of soliton solutions, the numerical solution might render a more generalized aspect in addressing versatile solutions for a wide range of arbitrary input pulses. Therefore, the SSFT scheme is efficiently employed to extract a plethora of optical solitons solutions such as kink waves, bright, dark, bright-dark, singular, singular periodic solitons. The obtained results, via MATLAB, are in total agreement with the findings explored form the exact analytical solutions. As a result, this numerical technique may provide a creditable mathematical tool to solve a wide range of other nonlinear evolution partial differential equations in the mathematical physics field.

Automated summary

In this study, the split-step Fourier transform (SSFT) method is used to analyze the complex Ginzburg-Landau (CGL) equation. Various types of optical soliton solutions are obtained using the numerical approach, and the results are found to be in agreement with the analytical solutions. This numerical technique can be applied to solve other nonlinear evolution partial differential equations in the field of mathematical physics.