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The world of the complex Ginzburg-Landau equation [PDF]
Reviews of Modern Physics, 2002 Submitted to Reviews of Modern Physics, reduced resolution ...
Aranson, Igor S., Kramer, Lorenz
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The inviscid limit for the complex Ginzburg–Landau equation
Journal of Mathematical Analysis and Applications, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Machihara, Shuji, Nakamura, Yoshihisa
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Optical solitons with complex Ginzburg–Landau equation
Nonlinear Dynamics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mirzazadeh, Mohammad +9 more
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Target waves in the complex Ginzburg-Landau equation
Physical Review E, 2000We 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, 2000This 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, 2010Taming 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, 2022zbMATH 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, 2006A 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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Potential for the Complex Ginzburg-Landau Equation
Europhysics Letters (EPL), 1990A 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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The complex Ginzburg–Landau equation: an introduction
Contemporary Physics, 2012The 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 +1 more
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