4 research outputs found
Two-dimensional structures in the quintic Ginzburg-Landau equation
By using ZEUS cluster at Embry-Riddle Aeronautical University we perform
extensive numerical simulations based on a two-dimensional Fourier spectral
method Fourier spatial discretization and an explicit scheme for time
differencing) to find the range of existence of the spatiotemporal solitons of
the two-dimensional complex Ginzburg-Landau equation with cubic and quintic
nonlinearities. We start from the parameters used by Akhmediev {\it et. al.}
and slowly vary them one by one to determine the regimes where solitons exist
as stable/unstable structures. We present eight classes of dissipative solitons
from which six are known (stationary, pulsating, vortex spinning, filament,
exploding, creeping) and two are novel (creeping-vortex propellers and spinning
"bean-shaped" solitons). By running lengthy simulations for the different
parameters of the equation, we find ranges of existence of stable structures
(stationary, pulsating, circular vortex spinning, organized exploding), and
unstable structures (elliptic vortex spinning that leads to filament,
disorganized exploding, creeping). Moreover, by varying even the two initial
conditions together with vorticity, we find a richer behavior in the form of
creeping-vortex propellers, and spinning "bean-shaped" solitons. Each class
differentiates from the other by distinctive features of their energy
evolution, shape of initial conditions, as well as domain of existence of
parameters.Comment: 19 pages, 19 figures, 8 tables, updated text and reference
Exploding soliton and front solutions of the complex cubic-quintic Ginzburg-Landau equation
We present a study of exploding soliton and front solutions of the complex cubic–quintic Ginzburg–Landau (CGLE) equation. We show that exploding fronts occur in a region of the parameter space close to that where exploding solitons exist. Explosions occur when eigenvalues in the linear stability analysis for the ground-state stationary solitons have positive real parts. We also study transition from exploding fronts to exploding solitons and observed extremely asymmetric soliton explosions. © 2005 Elsevier B.V. All rights reserved.The work of J.M.S.C. was supported by the Dirección General de Enseñanza Superior under contract BFM2003-00427.Peer Reviewe
Exploding Soliton and Front Solutions of the Complex Cubic-Quintic Ginzburg-Landau Equation
We present a study of exploding soliton and front solutions of the complex cubic-quintic Ginzburg-Landau (CGLE) equation. We show that exploding fronts occur in a region of the parameter space close to that where exploding solitons exist. Explosions occur when eigenvalues in the linear stability analysis for the ground-state stationary solitons have positive real parts. We also study transition from exploding fronts to exploding solitons and observed extremely asymmetric soliton explosions