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Stability of traveling waves for a conserved field

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  • Zimmermann, Walter

Abstract

The stability of traveling waves is investigated for a model describing the post threshold behavior beyond oscillatory instabilities for a class of systems with a conserved order parameter. Oscillatory instabilities and their post threshold behavior in systems with unconserved order parameters have been a central topic of nonlinear science during the recent decade. The most famous equation in this context is the Ginzburg-Landau equation with complex coefficients. Here I discuss a straight forward generalization of this Ginzburg-Landau equation which covers also spinodal decomposition and the crossover to an oscillatory instability for a globally conserved order parameter. Especially, the modification of the border to spatiotemporal chaos is considered, which is described by the so-called Benjamin-Feir resonance.

Suggested Citation

  • Zimmermann, Walter, 1997. "Stability of traveling waves for a conserved field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(3), pages 405-412.
    • Handle: RePEc:eee:phsmap:v:237:y:1997:i:3:p:405-412
    DOI: 10.1016/S0378-4371(96)00422-0
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    1. Hohenberg, Paul M., 1993. "Time and Order in Metropolitan Vienna: A Seizure of Schedule. By Robert Rotenberg. Washington, DC: Smithsonian Institution Press, 1992. Pp. x, 262. $32.50," The Journal of Economic History, Cambridge University Press, vol. 53(3), pages 668-669, September.
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