A novel technique to construct exact solutions for the complex Ginzburg-Landau equation using quadratic-cubic nonlinearity law

Abstract

The Complex Ginzburg-Landau equation (CGLE) has been suggested and investigated as a model for turbulent dynamics in nonlinear partial differential equations. It is a particularly intriguing model in this aspect since it is a dissipative form of the nonlinear Schrodinger equation. The model is studied with quadratic-cubic law nonlinear fiber by using Q6--model expansion method, bright, dark, dark-singular, singular, and dark-bright optical soliton solutions are obtained. The findings of this study might assist in comprehending some of the physical implications of various nonlinear physics models. The hyperbolic sine, for example, appears in the calculation of the Roche limit and gravitational potential of a cylinder, while The hyperbolic cosine function is the shape of a hanging cable (the so-called catenary). Finally, there are some discussions regarding new complex solutions. It is explored by giving physical meaning to the constants found in traveling wave solutions, which are both physically and mathematically significant. Three-dimensional simulations and contour plots are used to enhance these discussions.