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Simple examples of the derivation of amplitude equations for systems of equations possessing bifurcations

Published online by Cambridge University Press:  17 February 2009

A. J. Roberts
A. J. Roberts
Affiliation:
Department of Applied Mathematics, University of Adelaide, Adelaide, S.A. 5000
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Abstract

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The method of Coullet and Spiegel [3], which derives ordinary differential equations describing the time evolution of a system of partial differential equations when the system is near critical, is applied to some simple problems. These problems serve to illustrate simply many features of the method.

Type
Research Article
Information
The ANZIAM Journal , Volume 27 , Issue 1 , July 1985 , pp. 48 - 65
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Abramowitz, M. and Stegun, I. A., Handbook of mathematical functions (Dover, New York, 1965).Google Scholar
[2]Bender, C. M. and Orszag, S. A., Advanced mathematical methods for scientists and engineers (McGraw-Hill, New York, 1978).Google Scholar
[3]Coullet, P. H. and Spiegel, E. A., “Amplitud equations for systems with competing instabilities”, SIAM J. Appl. Math. 43 (1983), 776–821.CrossRefGoogle Scholar
[4]Roberts, A. J., “An introduction to the technique of reconstitution”, SIAM J. Math. Anal. (1985), (to appear).CrossRefGoogle Scholar