Influence of the higher-order effects on the solutions of the complex cubic–quintic Ginzburg–Landau equation
Ivan M. Uzunov, Svetoslav Nikolov
Abstract
The influence of intrapulse Raman scattering (IRS), self-steepening (SS) and third-order of dispersion (TOD) on the solutions of the complex cubic–quintic Ginzburg–Landau equation is studied by means of bifurcation analysis of the dynamical model. The numerical bifurcation diagram of the amplitude of the solution with respect to the nonlinear gain has revealed a cascade of bifurcations that leads to chaotic behaviour. We have found that the IRS leads to the larger shifts in positions and widths of the zones with different types of solutions in comparison to the influence of SS and TOD. Using numerical bifurcation diagrams of the amplitude of the solution with respect to the parameter describing IRS the following types of transformations have been identified: (a) from chaotic into two-periodic solution; (b) from two-periodic into a limit cycle; and (c) from a limit cycle into a stationary solution.