Global branches of multi-bump periodic solutions of the Swift-Hohenberg equation

In this paper we study the existence of single- and multi-bump periodic solutions of a class of fourth order ordinary differential equations arising in problems of pattern formation. Measuring the tendency to form patterns by a parameter q, we view the problem as a nonlinear eigenvalue problem. With...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2001-06, Vol.158 (2), p.91-153
Main Authors: VAN DEN BERG, G. J. B, PELETIER, L. A, TROY, W. C
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Inelasticity (thermoplasticity, viscoplasticity...)
Mathematical analysis
Mathematics
Ordinary differential equations
Physics
Sciences and techniques of general use
Solid mechanics
Structural and continuum mechanics
Viscoelasticity, plasticity, viscoplasticity
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Summary:In this paper we study the existence of single- and multi-bump periodic solutions of a class of fourth order ordinary differential equations arising in problems of pattern formation. Measuring the tendency to form patterns by a parameter q, we view the problem as a nonlinear eigenvalue problem. With the use of analytical as well as numerical methods, branches of periodic solutions are investigated, both locally and globally.[PUBLICATION ABSTRACT]
ISSN:0003-9527
1432-0673
DOI:10.1007/PL00004243