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Probing a subcritical instability with an amplitude expansion: An exploration of how far one can get by Paul Becherer; Alexander N. Morozov; Wim van Saarloos is a Physics and Astronomy article available to read on EtoBox.

What is Probing a subcritical instability with an amplitude expansion: An exploration of how far one can get about?

We explore methods to locate subcritical branches of spatially periodic solutions in pattern forming systems with a nonlinear finite-wavelength instability. We do so by means of a direct expansion in the amplitude of the linearly least stable mode about the appropriate reference state which one considers. This is motivated by the observation that for some equations fully nonlinear chaotic dynamics has been found to be organized around periodic solutions that do not simply bifurcate from the basic (laminar) state. We apply the method to two model equations, a subcritical generalization of the Swift-Hohenberg equation and a novel extension of the Kuramoto-Sivashinsky equation that we introduce to illustrate the abovementioned scenario in which weakly chaotic subcritical dynamics is organized around periodic states that bifurcate ''from infinity'' and that can nevertheless be probed perturbatively. We explore the reliability and robustness of such an expansion, with a particular focus on the use of these methods for determining the existence and approximate properties of finite-amplitude stationary solutions. Such methods obviously are to be used with caution: the expansions are often

Who reads Probing a subcritical instability with an amplitude expansion: An exploration of how far one can get?

Author

Paul Becherer; Alexander N. Morozov; Wim van Saarloos

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0167-2789)

Published

2009

Language

EN

Field

Physics and Astronomy (Physical Sciences)