Periodic spatio-temporal oscillations governed by a globally controlled Ginzburg–Landau equation

A new type of periodic oscillations in a globally controlled subcritical cubic complex Ginzburg–Landau equation, formerly observed in numerical simulations, is explained and investigated analytically by means of a multiscale perturbation theory. Using an appropriate class of solutions of the nonline...

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Bibliographic Details
Published in:Physica. D 2011-06, Vol.240 (12), p.1036-1040
Main Authors: Kanevsky, Y., Nepomnyashchy, A.A.
Format: Article
Language:English
Subjects:
Asymptotic properties
Complex Ginzburg–Landau equation
Dispersions
Exact sciences and technology
Feedback control
Focusing nonlinearity
Frequency shift
Mathematical analysis
Mathematical models
Nonlinearity
Oscillations
Perturbation theory
Physics
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Summary:A new type of periodic oscillations in a globally controlled subcritical cubic complex Ginzburg–Landau equation, formerly observed in numerical simulations, is explained and investigated analytically by means of a multiscale perturbation theory. Using an appropriate class of solutions of the nonlinear Schrödinger equation as a starting point, we construct a new class of asymptotic solutions of the cubic complex Ginzburg–Landau equation in the limit of large dispersion and nonlinear frequency shift. ► Adiabatic approximation is applied to nonzero genus solutions of perturbed NSE. ► New class of periodic solutions of globally controlled CGLE is found. ► Stability of obtained solutions is revealed numerically.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2011.03.001