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Periodic Solutions of the Complex Cubic-Quintic Ginzburg–Landau Equation in the Presence of Higher-Order Effects
Physics of Wave Phenomena ( IF 1.4 ) Pub Date : 2021-02-12 , DOI: 10.3103/s1541308x20040111
I. M. Uzunov , T. N. Arabadzhiev

Abstract

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.



中文翻译:

存在高阶效应的立方三次Quinzburg-Landau方程的周期解

摘要

我们已经从数值上研究了脉冲内拉曼散射(IRS)和自增强(SS)对复杂三次三次Ginzburg-Landau方程的周期2脉动解的影响。报告了在SS影响下数值解的级联变换,其中包括:1期解,混沌解,倍频变换导致出现具有多个周期的脉动解,然后减半变换,在tx解中呈周期性,最后均匀地平移前沿。我们已经表明,通过增加IRS参数,可以将与SS相关的周期为4的脉动解成功地转换为周期为2的,周期为1的脉动解,最后转换为平稳解。

更新日期:2021-02-15
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