Generation of pulse trains in nonlinear optical fibers through the generalized complex Ginzburg-Landau equation

2009 ◽  
Vol 80 (6) ◽  
Author(s):  
Camus G. Latchio Tiofack ◽  
Alidou Mohamadou ◽  
Timoléon C. Kofané ◽  
Alain B. Moubissi
Keyword(s):  
Optical Fibers ◽  
Nonlinear Optical ◽  
Landau Equation ◽  
Ginzburg Landau ◽  
Pulse Trains ◽  
Ginzburg Landau Equation ◽  
Generalized Complex

Dark soliton solutions of the cubic-quintic complex Ginzburg–Landau equation with high-order terms and potential barriers in normal-dispersion fiber lasers

2021 ◽  
Author(s):  
Marco A. Viscarra ◽  
Deterlino Urzagasti
Keyword(s):  
Optical Fibers ◽  
Landau Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Two Dimensions ◽  
Ginzburg Landau ◽  
Normal Dispersion ◽  
Homogeneous Solutions ◽  
Dark Solitons ◽  
Ginzburg Landau Equation

In this paper, we numerically study dark solitons in normal-dispersion optical fibers described by the cubic-quintic complex Ginzburg–Landau equation. The effects of the third-order dispersion, self-steepening, stimulated Raman dispersion, and external potentials are also considered. The existence, chaotic content and interactions of these objects are analyzed, as well as the tunneling through a potential barrier and the formation of dark breathers aside from dark solitons in two dimensions and their mutual interactions as well as with periodic potentials. Furthermore, the homogeneous solutions of the model and the conditions for their stability are also analytically obtained.

Analytic solutions for the generalized complex Ginzburg–Landau equation in fiber lasers

2017 ◽  
Vol 89 (4) ◽  
pp. 2933-2939 ◽  
Author(s):  
Wenjun Liu ◽  
Weitian Yu ◽  
Chunyu Yang ◽  
Mengli Liu ◽  
Yujia Zhang ◽  
...  
Keyword(s):  
Fiber Lasers ◽  
Landau Equation ◽  
Analytic Solutions ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Generalized Complex

scholarly journals Localized Pulsating Solutions of the Generalized Complex Cubic-Quintic Ginzburg-Landau Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Ivan M. Uzunov ◽  
Zhivko D. Georgiev
Keyword(s):  
Limit Cycle ◽  
Solitary Wave Solution ◽  
Landau Equation ◽  
Melnikov Method ◽  
Van Der Pol Oscillator ◽  
Unperturbed System ◽  
Van Der Pol ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Generalized Complex

We study the dynamics of the localized pulsating solutions of generalized complex cubic-quintic Ginzburg-Landau equation (CCQGLE) in the presence of intrapulse Raman scattering (IRS). We present an approach for identification of periodic attractors of the generalized CCQGLE. Using ansatz of the travelling wave and fixing some relations between the material parameters, we derive the strongly nonlinear Lienard-Van der Pol equation for the amplitude of the nonlinear wave. Next, we apply the Melnikov method to this equation to analyze the possibility of existence of limit cycles. For a set of fixed parameters we show the existence of limit cycle that arises around a closed phase trajectory of the unperturbed system and prove its stability. We apply the Melnikov method also to the equation of Duffing-Van der Pol oscillator used for the investigation of the influence of the IRS on the bandwidth limited amplification. We prove the existence and stability of a limit cycle that arises in a neighborhood of a homoclinic trajectory of the corresponding unperturbed system. The condition of existence of the limit cycle derived here coincides with the relation between the critical value of velocity and the amplitude of the solitary wave solution (Uzunov, 2011).

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