Electron. J. Differential Equations, Vol. 2017 (2017), No. 101, pp. 1-20.

On the dynamics of second-order Lagrangian systems

Ronald Adams, William D. Kalies, Robert C. A. M. Vandervorst

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
William D. Kalies
Department of Mathematics
Florida Atlantic University
Boca Raton, FL 33431, USA
email: wkalies@fau.edu
Robert C. A. M. Vandervorst
Department of Mathematics
VU University
Amsterdam, NL
email: vdvorst@few.vu.nl

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