Abstract
The present paper is devoted to the study of localized patterns in models in which a trivial homogeneous state is stable against infinitesimal disturbances, but can be triggered into a nontrivial oscillatory state by a finite disturbance. A well-Known example of a physical medium that demonstrates this property is a layer of a binary liquid heated from below, where oscillatory convection sets in via a subcritical bifurcation.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
V. I. Petviashvili and A. M. Sergeev, Spiral solitons in active media with an excitation threshold, Dokl. AN SSSR (Sov. Phys. — Doklady) 276:1380 (1964).
A. V. Klyachkin, Modulational instability and autowaves in active media described by nonlinear equations of the Ginzburg-Landau type, Preprint (1989).
B. A. Malomed, Evolution of nonsoliton and “quasicla-ssical” wavetrains in nonlinear Schrodinger and Korte-weg-de Vries equations with dissipative perturbations, Physica D, 39:155 (1987).
B. A. Malomed and A. A. Nepomnyashchy, Kinks and soli-tons in a generalized Ginzburg-Landau equation, Proc. of the IY Int. Workshop on Nonlinear and Turbulent Processes in Physics, Naukova Dumka, Kiev, 2:391 (1989).
B. A. Malomed, Nonsteady waves in distributed dynamical systems, Physica D 8:343 (1983).
O. Thual and S. Fauve, Localized structures generated by subcritical instabilities, J. Phys. 49:1829 (1988).
P. Kolodner, D. Bensimon, and C. M. Surko, Traveling-wave convection in an annulus, Phys. Rev. Lett. 60:1723 (1988).
A. Joets and R. Ribotta, Localized, time-dependent state in the convection of a nematic liquid crystal, Phys. Rev. Lett. 60:2164 (1988).
V. Hakim, P. Jakobsen, and Y. Pomeau, Fronts vs solitary waves in nonequilibrium systems, Preprint (1989).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Plenum Press, New York
About this chapter
Cite this chapter
Malomed, B.A., Nepomnyashchy, A.A. (1990). Kinks and Solitons in the Generalized Ginzburg-Landau Equation. In: Busse, F.H., Kramer, L. (eds) Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems. NATO ASI Series, vol 225. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5793-3_40
Download citation
DOI: https://doi.org/10.1007/978-1-4684-5793-3_40
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-5795-7
Online ISBN: 978-1-4684-5793-3
eBook Packages: Springer Book Archive