Bifurcations, stationary optical solitons and exact solutions for complex Ginzburg-Landau equation with nonlinear chromatic dispersion in non-Kerr law media

This paper obtains the stationary optical solitons and new exact solutions for complex Ginzburg-Landau equation (CGLE) with nonlinear chromatic dispersion and Kudryashov's reflective index structure in a non-Kerr law media. The research work is carried out according to the following route: first, the CGLE is transformed into a second order nonlinear ordinary differential equation by an appropriate substitution. Then, the bifurcation, stationary soliton solution and exact solution of CGLE are obtained by using dynamic system theory and polynomial complete discriminant system method. Abundant solutions are obtained, including periodic solutions, doubly-periodic solutions, hyperbolic function solutions, rational function solutions and exponential function solutions. Finally, the 3D and 2D graphics for the solutions are drawn. Since the appearance of stationary soliton means the stop of signal transmission, the research results provide a way to avoid the disaster of superconducting propagation in nonlinear media.

Automated summary

This paper transforms the complex Ginzburg-Landau equation (CGLE) into a second order nonlinear ordinary differential equation through an appropriate substitution, and obtains the bifurcation, stationary soliton solution and exact solution of CGLE by using dynamic system theory and polynomial complete discriminant system method. Abundant solutions are obtained, including periodic solutions, doubly-periodic solutions, hyperbolic function solutions, rational function solutions and exponential function solutions. Finally, the 3D and 2D graphics for the solutions are drawn. The research results provide a way to avoid the disaster of superconducting propagation in nonlinear media, as the appearance of stationary soliton means the stop of signal transmission.