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Multibump periodic travelling waves in suspension bridges

Published online by Cambridge University Press:  14 November 2011

L. A. Peletier  and
W. C. Troy
L. A. Peletier
Affiliation:
Mathematical Institute, Leiden University, PB 9512, 2300 RA, Leiden, The Netherlands
W. C. Troy
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.
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Abstract

We investigate different types of periodic solutions of a fourth-order, nonlinear differential equation, which has been proposed as a model for travelling waves in suspension bridges. We develop a shooting argument, which enables us to prove the existence of two families of multibump periodic solutions, each containing a countably infinite number of different solutions

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 3 , 1998 , pp. 631 - 659
Copyright
Copyright © Royal Society of Edinburgh 1998

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References

1Champneys, A. R. and McKenna, P. J.. On solitary waves of a piecewise-linear suspended beam model. Nonlinearity 10 (1997), 1763–82.Google Scholar
2Dananić, V. and Bjeliš, A.. Domain patterns in incommensurate systems with the uniaxial real order parameter. Phys. Rev. E 50 (1994), 3900–10.CrossRefGoogle ScholarPubMed
3Lazer, A. C. and McKenna, P. J.. Large-amplitude oscillations in suspension bridges: somenew connections with nonlinear analysis. SIAM Rev. 32 (1990), 537–78.CrossRefGoogle Scholar
4McKenna, P. J. and Chen, Y.. Numerical variational methods for approximating traveling waves in a nonlinearly suspended beam (Preprint).Google Scholar
5McKenna, P. J. and Walter, W.. Nonlinear oscillations in a suspension bridge. Arch. Rational Mech. Anal. 87 (1987), 167–77.CrossRefGoogle Scholar
6McKenna, P. J. and Walter, W.. Traveling waves in a suspension bridge. SIAM J. Appl. Math. 50 (1990), 703–15.Google Scholar
7Peletier, L. A. and Troy, W. C.. Spatial patterns described by the Extended Fisher–Kolmogorov (EFK) equation: Kinks. Differential Integral Equations 6 (1995), 1279–304.Google Scholar
8Peletier, L. A. and Troy, W. C.. Spatial patterns described by the Extended Fisher–Kolmogorov (EFK) equation: Periodic solutions. SIAM J. Math. Anal. 28 (1997), 1317–53.CrossRefGoogle Scholar
9Peletier, L. A. and Troy, W. C.. Chaotic solutions of the Extended Fisher–Kolmogorov (EFK) equation. J. Differential Equations 129 (1996), 458–508.CrossRefGoogle Scholar
10Peletier, L. A. and Troy, W. C.. A topological shooting method and the existence of kinksof the Extended Fisher–Kolmogorov equation. Topol. Methods Nonlinear Anal. 6 (1996), 331–55.CrossRefGoogle Scholar