Wound-up phase turbulence in the complex Ginzburg-Landau equation

Montagne, Raúl; Hernández-Garcı́a, Emilio; Amengual, A.; Miguel, M. San

doi:10.1103/physreve.56.151

Cited by 57 publications

(40 citation statements)

References 57 publications

(145 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The case of non-zero ν was pointed out by Montagne et al [63] and Torcini et al [31] on the basis of numerical simulations. Recently, this problem has been extensively studied by numerical analysis based on an equivalent ODE system [35].…”

Section: The Context Of Modulated Wavesmentioning

confidence: 99%

Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II. Convective/absolute transitions

Garnier¹,

Chiffaudel²,

Daviaud³

2003

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

We present experimental results on hydrothermal traveling-waves dynamics in long and narrow 1D channels. The onset of primary traveling-wave patterns is briefly presented for different fluid heights and for annular or bounded channels, i.e., within periodic or non-periodic boundary conditions. For periodic boundary conditions, by increasing the control parameter or changing the discrete mean-wavenumber of the waves, we produce modulated waves patterns. These patterns range from stable periodic phase-solutions, due to supercritical Eckhaus instability, to spatio-temporal defect-chaos involving traveling holes and/or counter-propagating-waves competition, i.e., traveling sources and sinks. The transition from non-linearly saturated Eckhaus modulations to transient pattern-breaks by traveling holes and spatiotemporal defects is documented. Our observations are presented in the framework of coupled complex Ginzburg-Landau equations with additional fourth and fifth order terms which account for the reflection symmetry breaking at high wave-amplitude far from onset. The second part of this paper [1] extends this study to spatially non-periodic patterns observed in both annular and bounded channel.

show abstract

Section: The Context Of Modulated Wavesmentioning

confidence: 99%

Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II. Convective/absolute transitions

Garnier¹,

Chiffaudel²,

Daviaud³

2003

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…8(c). Vortex solitons with integer topological charge m can be looked for as E(r, φ) = E 0 (r)e imφ , where (r, φ) are polar coordinates with the origin at the pivot of the vortex [40,43,[45][46][47][48]. The fundamental 2D soliton corresponds to m = 0, with the maximum at the origin.…”

Section: Two-dimensional Self-localized Solutions: Stripes Fundammentioning

confidence: 99%

From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency-selective feedback

et al. 2011

View full text Add to dashboard Cite

We use the cubic complex Ginzburg-Landau equation coupled to a dissipative linear equation as a model of lasers with an external frequency-selective feedback. It is known that the feedback can stabilize the one-dimensional (1D) self-localized mode. We aim to extend the analysis to 2D stripe-shaped and vortex solitons. The radius of the vortices increases linearly with their topological charge, m, therefore the flat-stripe soliton may be interpreted as the vortex with m = ∞, while vortex solitons can be realized as stripes bent into rings. The results for the vortex solitons are applicable to a broad class of physical systems. There is a qualitative agreement between our results and those recently reported for models with saturable nonlinearity.

show abstract

“…1 using a numerical scheme described in detail in Ref. [13]. The method is pseudospectral and second-order accurate in time, and is similar to the so-called two-step method.…”

Section: Numerical Resultsmentioning

confidence: 99%

Patterns arising from the interaction between scalar and vectorial instabilities in two-photon resonant Kerr cavities

et al. 2002

View full text Add to dashboard Cite

We study pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a nonlinear Kerr medium close to a two-photon resonance, placed inside a ring cavity with flat mirrors and driven by a coherentx-polarized plane-wave field. In the self-focusing case, for negative detunings the pattern arises naturally from a codimension two bifurcation. For a critical value of the field intensity there are two wave numbers that become unstable simultaneously, corresponding to two Turing-like instabilities. Considered alone, one of the instabilities would originate a linearly polarized hexagonal pattern whereas the other instability is of pure vectorial origin and would give rise to an elliptically polarized stripe pattern. We show that the competition between the two wavenumbers can originate different structures, being the detuning a natural selection parameter.

show abstract

Wound-up phase turbulence in the complex Ginzburg-Landau equation

Cited by 57 publications

References 57 publications

Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II. Convective/absolute transitions

Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II. Convective/absolute transitions

From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency-selective feedback

Patterns arising from the interaction between scalar and vectorial instabilities in two-photon resonant Kerr cavities

Contact Info

Product

Resources

About