Periodic Solutions of the Complex Cubic-Quintic Ginzburg-Landau Equation in the Presence of Higher-Order Effects

摘要

We have studied numerically the influence of intrapulse Raman scattering (IRS) and self-steepening (SS) on the period-2 pulsating solution of the complex cubic-quintic Ginzburg-Landau equation. A cascade of transformations of the numeric solutions under the influence of SS is reported, which includes the existence of: period-1 solutions, chaotic solutions, period-doubling transformation leading to the appearance of pulsating solutions with many periods, then period-halved transformation, periodic in t and x solutions and, finally, uniformly translating fronts. We have shown that by increasing the IRS parameter, the period-4 pulsating solution related to the SS can be successfully transformed into a period-2, period-1 pulsating solutions and, finally, into a stationary solution.