Results 21 to 30 of about 22,195 (121)

Soliton turbulences in the complex Ginzburg-Landau equation

, 2007
We study spatio-temporal chaos in the complex Ginzburg-Landau equation in parameter regions of weak amplification and viscosity. Turbulent states involving many soliton-like pulses appear in the parameter range, because the complex Ginzburg-Landau ...
G. P. Agrawal, Hidetsugu Sakaguchi, P. Manneville, T. Bohr, U. Frisch, Y. Kuramoto   +5 more
core   +1 more source

Defect Chaos of Oscillating Hexagons in Rotating Convection

, 1999
Using coupled Ginzburg-Landau equations, the dynamics of hexagonal patterns with broken chiral symmetry are investigated, as they appear in rotating non-Boussinesq or surface-tension-driven convection. We find that close to the secondary Hopf bifurcation
A. M. Soward, A. Torcini, A. Torcini, B. Echebarria, B. Echebarria, Blas Echebarria, F. Busse, F. Busse, G. Ahlers, G. Grinstein, G. Huber, G. Küppers, H. Chaté, Hermann Riecke, J. Burguete, J. Lauzeral, J. Millán-Rodríguez, J. Swift, M. C. Cross, M. Dennin, M. Treiber, P. Coullet, P. Manneville, R. B. Hoyle, R. Montagne, S. Popp, S. W. Morris, Y. C. Hu   +27 more
core   +1 more source

Finite-parameter feedback control for stabilizing the complex Ginzburg-Landau equation [PDF]

, 2017
In this paper, we prove the exponential stabilization of solutions for complex Ginzburg-Landau equations using finite-parameter feedback control algorithms, which employ finitely many volume elements, Fourier modes or nodal observables (controllers).
Kalantarova, Jamila, Özsarı, Türker
core   +2 more sources

Thermodynamic Limit Of The Ginzburg-Landau Equations

, 1993
We investigate the existence of a global semiflow for the complex Ginzburg-Landau equation on the space of bounded functions in unbounded domain. This semiflow is proven to exist in dimension 1 and 2 for any parameter values of the standard cubic ...
Babin A V, Collet P, Collet P, Duan J, Duan J, Duan J, Eckhaus W, Friedman A, Henry D, Iooss G, Iooss G, Kato T, Matkowsky B J, Mielke A, Newell A, P Collet, Pazy A, Schneider G, Segel L, Solonnikov V A, van Harten A, Yang Y   +21 more
core   +2 more sources

On elliptic solutions of the cubic complex one-dimensional Ginzburg-Landau equation

, 2005
The cubic complex one-dimensional Ginzburg-Landau equation is considered. Using the Hone's method, based on the use of the Laurent-series solutions and the residue theorem, we have proved that this equation has neither elliptic standing wave nor elliptic
A. N. W. Hone, E. Fan, E. I. Timoshkova, E. I. Timoshkova, F. Cariello, G. P. Agrawal, G. S. Santos, I. Aranson, K. Nozaki, L. A. Takhtadzhyan, L. Brusch, M. C. Cross, M. Hecke van, M. Hecke van, M. J. Ablowitz, M. Musette, N. A. Kudryashov, N. A. Kudryashov, N. N. Akhmediev, P. Painleve, R. Conte, R. Conte, R. Conte, S. Yu. Vernov, S. Yu. Vernov, S. Yu. Vernov, V. A. Vladimirov, V. L. Ginzburg, W. Saarloos van   +28 more
core   +3 more sources

Relative Periodic Solutions of the Complex Ginzburg-Landau Equation

, 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   +2 more sources

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

, 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   +5 more sources

Modeling small‐angle scattering data of porous and/or bicontinuous structures in n dimensions

Journal of Applied Crystallography, EarlyView.
A small‐angle scattering fitting function is derived for porous materials with arbitrary fractal dimension. It includes a correlation peak and a power law at higher q.Fractal structures are often observed in small‐angle scattering experiments where a simple power law q−α describes the scattering intensity over many orders of magnitude.
Henrich Frielinghaus
wiley   +1 more source

Exact Phase Solutions of Nonlinear Oscillators on Two-dimensional Lattice

, 2003
We present various exact solutions of a discrete complex Ginzburg-Landau (CGL) equation on a plane lattice, which describe target patterns and spiral patterns and derive their stability criteria.
Aranson I. S., Aranson I. S., Guckenheimer J., Mori S., Nozaki K., Strogatz S. H., Yamada H.   +6 more
core   +2 more sources

Bekki-Nozaki Amplitude Holes in Hydrothermal Nonlinear Waves [PDF]

, 1999
We present and analyze experimental results on the dynamics of hydrothermal waves occuring in a laterally-heated fluid layer. We argue that the large-scale modulations of the waves are governed by a one-dimensional complex Ginzburg-Landau equation (CGLE).
Burguete, Javier, Chate, Hugues, Daviaud, Francois, Mukolobwiez, Nathalie   +3 more
core   +3 more sources