Results 41 to 50 of about 23,473 (246)
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
ON THE COMPLEX GINZBURG–LANDAU EQUATION WITH A DELAYED FEEDBACK [PDF]
Mathematical Models and Methods in Applied Sciences, 2006 We show how to stabilize the uniform oscillations of the complex Ginzburg–Landau equation with periodic boundary conditions by means of some global delayed feedback. The proof is based on an abstract pseudo-linearization principle and a careful study of the spectrum of the linearized operator.
Casal, A. C., Díaz, J. I.
openaire +1 more source
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
Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation [PDF]
, 2003 It is well known that pulse-like solutions of the cubic complex Ginzburg-Landau equation are unstable but can be stabilised by the addition of quintic terms.
A. Mecozzi +50 more
core +1 more source
Modulation equations near the Eckhaus boundary: the KdV equation [PDF]
, 2018 We are interested in the description of small modulations in time and space of wave-train solutions to the complex Ginzburg-Landau equation \begin{align*} \partial_T \Psi = (1+ i \alpha) \partial_X^2 \Psi + \Psi - (1+i \beta ) \Psi |\Psi|^2, \end{align*}
de Rijk, Björn +2 more
core +3 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 +1 more
doaj +1 more source
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 +5 more
doaj +1 more source
Integrability and chaotic dynamics in nonlinear dispersive stochastic model
Results in Applied MathematicsThis 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 +3 more
doaj +1 more source