Results 151 to 160 of about 978 (180)

Target waves in the complex Ginzburg-Landau equation

Physical Review E, 2000
We introduce a spatially localized inhomogeneity into the two-dimensional complex Ginzburg-Landau equation. We observe that this can produce two types of target wave patterns: stationary and breathing. In both cases, far from the target center, the field variables correspond to an outward propagating periodic traveling wave.
, Hendrey, , Nam, , Guzdar, , Ott
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Inviscid Limits¶of the Complex Ginzburg–Landau Equation

Communications in Mathematical Physics, 2000
This paper is devoted to the inviscid limit of the generalized complex Ginzburg-Landau (CGL) equation: \[ \begin{cases}\partial_t u=(a+i\nu)\Delta_x u+Ru-(b+i\mu)f(u)\;\text{in} \Omega,\;t>0\\ U(x,0)=u_0(x),\quad x\in\Omega.\end{cases}\tag{1} \] The authors consider (1) in the whole space \(\Omega=\mathbb{R}^d\) as well as in the torus \(T^d=(\mathbb{R}
Bechouche, Philippe, Jüngel, Ansgar
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Taming turbulence in the complex Ginzburg-Landau equation

Physical Review E, 2010
Taming turbulence in the complex Ginzburg-Landau equation (CGLE) by using a global feedback control method and choosing traveling-wave solutions as our target state is investigated. The problem of optimal control for the smallest driving strength is studied by systematically comparing the stabilities of all traveling waves.
Meng, Zhan, Wei, Zou, Xu, Liu
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Spatial homogenization by perturbation on the complex Ginzburg–Landau equation

Japan Journal of Industrial and Applied Mathematics, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shun Ito, Hirokazu Ninomiya
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Synchronization in nonidentical complex Ginzburg-Landau equations

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2006
A cross-correlation coefficient of complex fields has been investigated for diagnosing spatiotemporal synchronization behavior of coupled complex fields. We have also generalized the subsystem synchronization way established in low-dimensional systems to one- and two-dimensional Ginzburg-Landau equations.
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The complex Ginzburg–Landau equation: an introduction

Contemporary Physics, 2012
The complex Ginzburg–Landau equation (CGLE), probably the most celebrated nonlinear equation in physics, describes generically the dynamics of oscillating, spatially extended systems close to the onset of oscillations. Using symmetry arguments, this article gives an easy access to this equation and an introduction into the rich spatio-temporal ...
Vladimir García-Morales, Katharina Krischer   +1 more
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On the invariants of the complex Ginzburg-Landau equation

Physics Letters A, 1984
Abstract Using Lie group theory, both the invariants and the similarity variables of the complex Ginzburg—Landau equation Vxx = a(Vt + bV) + cV|V|2kwherea,b,cϵIandkϵI are constructed.
Michael Magen, Philip Rosenau
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Potential for the Complex Ginzburg-Landau Equation

Europhysics Letters (EPL), 1990
A generalized thermodynamic potential is derived for spatially extended pattern-forming nonequilibrium systems whose order parameter obeys the complex Ginzburg-Landau equation in one spatial dimension. The real potential, generalizing the Ginzburg-Landau free energy, is shown to describe typical nonequilibrium phenomena like the Newell-Kuramoto and the
R Graham, T Tél
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Lattice Boltzmann model for the complex Ginzburg-Landau equation

Physical Review E, 2010
A lattice Boltzmann model with complex distribution function for the complex Ginzburg-Landau equation (CGLE) is proposed. By using multiscale technique and the Chapman-Enskog expansion on complex variables, we obtain a series of complex partial differential equations. Then, complex equilibrium distribution function and its complex moments are obtained.
Jianying, Zhang, Guangwu, Yan
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Dynamics of the globally coupled complex Ginzburg-Landau equation

Physical Review A, 1992
A discrete version of the complex Ginzburg-Landau equation is studied on a completely connected lattice of N sites. This can equivalently be described as a model of N identical globally coupled limit-cycle oscillators. The phase diagram is obtained by a combination of numerical and analytical techniques.
, Hakim, , Rappel
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