Results 11 to 20 of about 23,473 (246)

Nonequilibrium Dynamics in the Complex Ginzburg-Landau Equation [PDF]

Physical Review E, 2001
We present results from a comprehensive analytical and numerical study of nonequilibrium dynamics in the 2-dimensional complex Ginzburg-Landau (CGL) equation.
A. Weber, A.J. Bray, A.J. Bray, A.J. Bray, A.N. Pargellis, B. Yurke, F. Rojas, G.F. Mazenko, G.F. Mazenko, G.F. Mazenko, H. Chate, H. Chate, H. Toyoki, I.S. Aranson, K. Binder, M. C. Cross, M.C. Cross, P.S. Hagan, S. K. Das, S. Puri, Sanjay Puri, Subir K. Das, T. Ohta, W. van Saarloos, Y. Kuramoto   +24 more
core   +7 more sources

Bistability in the Complex Ginzburg-Landau Equation with Drift [PDF]

Physica D: Nonlinear Phenomena, 2009
Properties of the complex Ginzburg-Landau equation with drift are studied focusing on the Benjamin-Feir stable regime. On a finite interval with Neumann boundary conditions the equation exhibits bistability between a spatially uniform time-periodic state
Aranson, Brusch, Cash, Chaté, Cowley, Cross, Deissler, E. Knobloch, Eckhardt, Golubitsky, Guckenheimer, Kerswell, M.R.E. Proctor, Proctor, Rosenblat, S.M. Houghton, S.M. Tobias, Schilder, Schilder, Stewartson, Tobias, Tobias, Tobias, van Hecke   +23 more
core   +3 more sources

Standing waves of the complex Ginzburg-Landau equation [PDF]

Nonlinear Analysis: Theory, Methods & Applications, 2013
We prove the existence of nontrivial standing wave solutions of the complex Ginzburg-Landau equation $\phi_t = e^{i\theta} \Delta \phi + e^{i\gamma} |\phi |^\alpha \phi $ with periodic boundary conditions. Our result includes all values of $\theta $ and $
Cazenave, Thierry, Dickstein, Flávio, Weissler, Fred B.   +2 more
core   +5 more sources

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

Communications in Mathematical Physics, 1998
We study the set of solutions of the complex Ginzburg-Landau equation in $\real^d, d\OO(\log(1/\epsilon))$Comment: 24 ...
Collet, Pierre, Eckmann, Jean-Pierre
core   +4 more sources

Finite-time blowup for a complex Ginzburg-Landau equation [PDF]

SIAM Journal on Mathematical Analysis, 2012
We prove that negative energy solutions of the complex Ginzburg-Landau equation $e^{-i\theta} u_t = \Delta u+ |u|^{\alpha} u$ blow up in finite time, where \alpha >0 and \pi ...
Caffarelli L., Flávio Dickstein, Fred B. Weissler, Kato T., Kavian O., Levermore C.D., Ogawa T., Thierry Cazenave, Zakharov V.E.   +8 more
core   +9 more sources

Bi-Lipschitz Mané projectors and finite-dimensional reduction for complex Ginzburg-Landau equation. [PDF]

Proc Math Phys Eng Sci, 2020
Kostianko A.
europepmc   +3 more sources

Relative Periodic Solutions of the Complex Ginzburg-Landau Equation [PDF]

SIAM Journal on Applied Dynamical Systems, 2005
A method of finding relative periodic orbits for differential equations with continuous symmetries is described and its utility demonstrated by computing relative periodic solutions for the one-dimensional complex Ginzburg-Landau equation (CGLE) with ...
Dang‐Vu H., Lan Yueheng, Levenberg Kenneth, Michael T. Heath, Miller Willard, Philip Boyland, Robert D. Moser, Vanessa López   +7 more
core   +3 more sources

Dynamics of Defects in the Vector Complex Ginzburg-Landau Equation [PDF]

Physica D: Nonlinear Phenomena, 2001
Coupled Ginzburg-Landau equations appear in a variety of contexts involving instabilities in oscillatory media. When the relevant unstable mode is of vectorial character (a common situation in nonlinear optics), the pair of coupled equations has special ...
Amengual, Aranson, Aranson, Aranson, Bhandari, Coullet, Cross, Eguiluz, Eguiluz, Emilio Hernández-Garcı́a, Etrich, Firth, Gallego, Gil, Gil, Gomila, Hagan, Hendrey, Hernández-Garcı́a, Hernández-Garcı́a, Hoyuelos, Lega, Leggett, Maxi San Miguel, Michaelis, Miguel Hoyuelos, Montagne, Montagne, Montagne, Oppo, Pere Colet, Pismen, Pismen, San Miguel, Staliunas, Staliunas, Tlidi, Yang   +37 more
core   +4 more sources

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 ...
Vı́ctor M. Eguı́luz, Emilio Hernández-Garcı́a, Oreste Piro   +2 more
openalex   +6 more sources

Multisoliton Solutions of the Complex Ginzburg-Landau Equation [PDF]

Physical Review Letters, 1997
We present novel stable solutions which are soliton pairs and trains of the ID complex Ginzburg-Landau equation (CGLE), and analyze them. We propose that the distance between the pulses and the phase difference between them is defined by energy and momentum balance equations.
Akhmediev, N., Ankiewicz, A., Soto Crespo, J. M.   +2 more
openaire   +2 more sources