Instabilities of the Ginzburg-Landau equation: periodic solutions
Open Access
- 1 January 1986
- journal article
- Published by American Mathematical Society (AMS) in Quarterly of Applied Mathematics
- Vol. 44 (1) , 49-58
- https://doi.org/10.1090/qam/840442
Abstract
The evolution of spatially periodic unstable solutions to the Ginzburg-Landau equation is considered. These solutions are shown to remain pointwise bounded (Lagrange stable). The first step in the route to chaos is limit cycle behavior. This is treated by perturbation theory and shown to result in a factorable form. Agreement between the perturbation result and an exact numerical integration is shown to be excellent.Keywords
This publication has 20 references indexed in Scilit:
- Noise-sustained structure, intermittency, and the Ginzburg-Landau equationJournal of Statistical Physics, 1985
- Recurrence Phenomena and the Number of Effective Degrees of Freedom in Nonlinear Wave MotionsPublished by Cambridge University Press (CUP) ,1983
- Intermittency through modulational instabilityPhysics Letters A, 1983
- Chaos in a Perturbed Nonlinear Schrödinger EquationPhysical Review Letters, 1983
- Three-Frequency Motion and Chaos in the Ginzburg-Landau EquationPhysical Review Letters, 1982
- The Eckhaus and Benjamin-Feir resonance mechanismsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1978
- On three-dimensional packets of surface wavesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1974
- Finite bandwidth, finite amplitude convectionJournal of Fluid Mechanics, 1969
- The disintegration of wave trains on deep water Part 1. TheoryJournal of Fluid Mechanics, 1967
- Studies in Non-Linear Stability TheoryMathematics of Computation, 1966