Results 41 to 50 of about 2,507 (215)

Extensive Properties of the Complex Ginzburg-Landau Equation [PDF]

Communications in Mathematical Physics, 1999
We study the set of solutions of the complex Ginzburg-Landau equation in $\real^d, d<3$. We consider the global attracting set (i.e., the forward map of the set of bounded initial data), and restrict it to a cube $Q_L$ of side $L$. We cover this set by a (minimal) number $N_{Q_L}(ε)$ of balls of radius $ε$ in $\Linfty(Q_L)$.
Collet, Pierre, Eckmann, Jean-Pierre
openaire   +3 more sources

Response solution to complex Ginzburg–Landau equation with quasi-periodic forcing of Liouvillean frequency

Boundary Value Problems, 2020
In this paper, the existence of a response solution with the Liouvillean frequency vector to the quasi-periodically forced complex Ginzburg–Landau equation, whose linearized system is elliptic–hyperbolic, is obtained. The proof is based on constructing a
Shimin Wang, Jie Liu
doaj   +1 more source

Complex Ginzburg-Landau equation in the presence of walls and corners [PDF]

Physical Review E, 2001
We investigate the influence of walls and corners (with Dirichlet and Neumann boundary conditions) in the evolution of twodimensional autooscillating fields described by the complex Ginzburg-Landau equation. Analytical solutions are found, and arguments provided, to show that Dirichlet walls introduce strong selection mechanisms for the wave pattern ...
Eguíluz, Víctor M., Hernández-García, Emilio, Piro, Oreste   +2 more
openaire   +4 more sources

Motion of spiral waves in the complex Ginzburg–Landau equation [PDF]

Physica D: Nonlinear Phenomena, 2010
Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered. For parameters close to the vortex limit, and for a system of spiral waves with well-separated centres, laws of motion of the centres are found which vary depending on the order of magnitude of the separation of the centres.
Aguareles, M, Chapman, S, Witelski, T
openaire   +2 more sources

Phase dynamics in the complex Ginzburg–Landau equation

Journal of Differential Equations, 2004
For suitable parameter values, stable time periodic solutions of a special type form the locally preferred platform for the complex Ginzburg-Landau equation. An evolution equation is derived in a formal manner that describes the spatial global behavior for a local wave number. This local wave number is an approximate solution of a conservation law, and
Melbourne, Ian, Schneider, Guido
openaire   +1 more source

Dynamics of Fractional Stochastic Ginzburg–Landau Equation Driven by Nonlinear Noise

Mathematics, 2022
In this work, we focus on the long-time behavior of the solutions of the stochastic fractional complex Ginzburg–Landau equation defined on Rn with polynomial drift terms of arbitrary order.
Hong Lu, Linlin Wang, Mingji Zhang
doaj   +1 more source

Local dynamics of laser chain model with optoelectronic delayed unidirectional coupling [PDF]

Известия высших учебных заведений: Прикладная нелинейная динамика, 2022
Purpose. The local dynamics of the laser chain model with optoelectronic delayed unidirectional coupling is investigated. A system of equations is considered that describes the dynamics of a closed chain of a large number of lasers with optoelectronic ...
Grigorieva, Elena Viktorovna, Kashchenko, Sergej Aleksandrovich   +1 more
doaj   +1 more source

Integrability and chaotic dynamics in nonlinear dispersive stochastic model

Results in Applied Mathematics
This paper focuses on obtaining exact solutions and dynamical analysis of the stochastic real-valued Ginzburg–Landau equation driven by multiplicative Itô noise.
Muhammad Aziz-ur-Rehman, Muhammad Moneeb Tariq, Ayesha Zafar, Muhammad Bilal Riaz   +3 more
doaj   +1 more source

Highly Dispersive Optical Soliton Perturbation, with Maximum Intensity, for the Complex Ginzburg–Landau Equation by Semi-Inverse Variation

Mathematics, 2022
This work analytically recovers the highly dispersive bright 1–soliton solution using for the perturbed complex Ginzburg–Landau equation, which is studied with three forms of nonlinear refractive index structures.
Anjan Biswas, Trevor Berkemeyer, Salam Khan, Luminita Moraru, Yakup Yıldırım, Hashim M. Alshehri   +5 more
doaj   +1 more source

Global attractors for the complex Ginzburg–Landau equation

Journal of Mathematical Analysis and Applications, 2014
This paper studies the following initial-boundary value for the complex Ginzburg-Landau equation \[ \begin{aligned} \frac{\partial u}{\partial t}-(\lambda+i \alpha)\Delta & u+(\kappa+i\beta)|u|^{p-2}u-\gamma u=0,\;\;(x,t)\in \Omega\times \mathbb{R}^+,\\ & u=0,\;\;(x,t)\in \partial \Omega\times \mathbb{R}^+,\\ & u(x,0)=u_0(x),\;\;x \in \Omega,\end ...
Li, Fang, You, Bo
openaire   +2 more sources