Ronald Adams, William D. Kalies, Robert C. A. M. Vandervorst
Abstract:
In this article we are concerned with improving the twist condition for
second-order Lagrangian systems. We characterize a local Twist property
and demonstrate how results on the existence of simple closed
characteristics can be extended in the case of the Swift-Hohenberg / extended
Fisher-Kolmogorov Lagrangian. Finally, we describe explicit evolution
equations for broken geodesic curves that could be used to investigate
more general systems or closed characteristics.
Submitted October 6, 2016. Published April 11, 2017.
Math Subject Classifications: 37J45, 34C25, 47J30.
Key Words: Second-order Lagrangian; closed characteristic; twist system;
curve evolution.
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Ronald Adams Department of Mathematics Embry-Riddle Aeronautical University Daytona Beach, FL 32114, USA email: adamsr25@erau.edu |
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William D. Kalies Department of Mathematics Florida Atlantic University Boca Raton, FL 33431, USA email: wkalies@fau.edu |
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Robert C. A. M. Vandervorst Department of Mathematics VU University Amsterdam, NL email: vdvorst@few.vu.nl |
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