Construction of a Blow-Up Solution for the Complex Ginzburg–Landau Equation in a Critical Case
Sign Up to like & getrecommendations! Published in 2017 at "Archive for Rational Mechanics and Analysis"
DOI: 10.1007/s00205-017-1211-3
Abstract: We construct a solution for the Complex Ginzburg–Landau equation in a critical case which blows up in finite time T only at one blow-up point. We also give a sharp description of its profile. The… read more here.
Keywords: solution complex; complex ginzburg; ginzburg landau; equation critical ... See more keywords
Exponential Runge–Kutta Method for Two-Dimensional Nonlinear Fractional Complex Ginzburg–Landau Equations
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Scientific Computing"
DOI: 10.1007/s10915-020-01240-x
Abstract: In this work, we study numerically two-dimensional nonlinear spatial fractional complex Ginzburg–Landau equations. A centered finite difference method is exploited to discretize the spatial variables and leads to a system of the ordinary differential equation,… read more here.
Keywords: fractional complex; complex ginzburg; ginzburg landau; method ... See more keywords
Amplitude death criteria for coupled complex Ginzburg–Landau systems
Sign Up to like & getrecommendations! Published in 2019 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-019-04961-3
Abstract: Amplitude death, which occurs in a system when one or more macroscopic wavefunctions collapse to zero, has been observed in mutually coupled solid-state lasers, analog circuits, and thermoacoustic oscillators, to name a few applications. While… read more here.
Keywords: complex ginzburg; death; amplitude death; ginzburg landau ... See more keywords
Coupled complex Ginzburg–Landau systems with saturable nonlinearity and asymmetric cross-phase modulation
Sign Up to like & getrecommendations! Published in 2017 at "Annals of Physics"
DOI: 10.1016/j.aop.2018.07.003
Abstract: Abstract We formulate and study dynamics from a complex Ginzburg–Landau system with saturable nonlinearity, including asymmetric cross-phase modulation (XPM) parameters. Such equations can model phenomena described by complex Ginzburg–Landau systems under the added assumption of… read more here.
Keywords: ginzburg landau; ginzburg; complex ginzburg; saturable nonlinearity ... See more keywords
Dark-singular combo optical solitons with fractional complex Ginzburg-Landau equation
Sign Up to like & getrecommendations! Published in 2018 at "Optik"
DOI: 10.1016/j.ijleo.2018.06.076
Abstract: Abstract This paper employs dextended Jacobi's elliptic function expansion method to retrieve doubly periodic function as solutions to the stochastic complex Ginzburg–Landau equation. In the limiting case, when the modulus of ellipticity approaches unity, these… read more here.
Keywords: complex ginzburg; ginzburg landau; optical solitons; singular combo ... See more keywords
Comments on “Application of the first integral method for solving (1 + 1) dimensional cubic–quintic complex Ginzburg–Landau equation, Optik 164 (2018) 210–217″
Sign Up to like & getrecommendations! Published in 2019 at "Optik"
DOI: 10.1016/j.ijleo.2018.12.014
Abstract: Abstract In their recently published article, G. Akram et al. investigated (1 + 1) dimensional cubic–quintic complex Ginzburg–Landau equation and constructed its exact solutions via the first integral method. We argue that all of solutions obtained by… read more here.
Keywords: ginzburg landau; dimensional cubic; cubic quintic; equation ... See more keywords
Recurrent motion in the fractional complex Ginzburg–Landau equation
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DOI: 10.1063/1.5131376
Abstract: This article concerns recurrent motion in the fractional complex Ginzburg–Landau equation with a small recurrent force. By using Galerkin’s method and energy estimate method, we obtain the existence of the bounded solutions, periodic solutions, quasiperiodic… read more here.
Keywords: fractional complex; motion fractional; complex ginzburg; ginzburg landau ... See more keywords
Random attractor of stochastic complex Ginzburg–Landau equation with multiplicative noise on unbounded domain
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DOI: 10.1080/07362994.2016.1259075
Abstract: ABSTRACT The existence of a compact random attractor for the stochastic complex Ginzburg–Landau equation with multiplicative noise has been investigated on unbounded domain. The solutions are considered in suitable spaces with weights. According to crucial… read more here.
Keywords: complex ginzburg; ginzburg landau; stochastic complex; random attractor ... See more keywords
Upper semicontinuity of random attractors of stochastic discrete complex Ginzburg–Landau equations with time-varying delays in the delay
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Difference Equations and Applications"
DOI: 10.1080/10236198.2018.1437913
Abstract: Abstract A system of stochastic discrete complex Ginzburg–Landau equations with time-varying delays is considered. We first prove the existence and uniqueness of random attractor for these equations. Then, we analyze the convergence properties of the… read more here.
Keywords: complex ginzburg; discrete complex; ginzburg landau; time ... See more keywords
Spectral stability of pattern-forming fronts in the complex Ginzburg–Landau equation with a quenching mechanism
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DOI: 10.1088/1361-6544/ac355b
Abstract: We consider pattern-forming fronts in the complex Ginzburg–Landau equation with a traveling spatial heterogeneity which destabilises, or quenches, the trivial ground state while progressing through the domain. We consider the regime where the heterogeneity propagates… read more here.
Keywords: complex ginzburg; forming fronts; pattern forming; equation ... See more keywords
Discrete and periodic complex Ginzburg-Landau equation for a hydrodynamic active lattice.
Sign Up to like & getrecommendations! Published in 2021 at "Physical review. E"
DOI: 10.1103/physreve.103.062215
Abstract: A discrete and periodic complex Ginzburg-Landau equation, coupled to a mean equation, is systematically derived from a driven and dissipative lattice oscillator model, close to the onset of a supercritical Andronov-Hopf bifurcation. The oscillator model… read more here.
Keywords: landau equation; ginzburg landau; equation; periodic complex ... See more keywords