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Scaling Laws and Bifurcation

Part of the Lecture Notes in Mathematics book series (LNM,volume 1463)

Abstract

Equations with symmetry often have solution branches which are related by a simple rescaling. This property can be expressed in terms of a scaling law which is similar to the equivariance condition except that it also involves the parameters of the problem. We derive a natural context for the existence of such scaling laws based on the symmetry of the problem and show how bifurcation points can also be related by a scaling. This leads in some cases, to a proof of existence of bifurcating branches at a mode interaction. The results are illustrated for the Kuramoto-Sivashinsky equation.

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© 1991 Springer-Verlag

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Aston, P.J. (1991). Scaling Laws and Bifurcation. In: Roberts, M., Stewart, I. (eds) Singularity Theory and its Applications. Lecture Notes in Mathematics, vol 1463. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085423

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  • DOI: https://doi.org/10.1007/BFb0085423

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53736-6

  • Online ISBN: 978-3-540-47047-2

  • eBook Packages: Springer Book Archive