Periodic orbits in nonlinear wave equations on networks
Por:
Caputo, J. G., Khames, I., Knippel, A., Panayotaros, P.
Publicada:
15 sep 2017
Resumen:
We consider a cubic nonlinear wave equation on a network and show that
inspecting the normal modes of the graph, we can immediately identify
which ones extend into nonlinear periodic orbits. Two main classes of
nonlinear periodic orbits exist: modes without soft nodes and others.
For the former which are the Goldstone and the bivalent modes, the
linearized equations decouple. A Floquet analysis was conducted
systematically for chains; it indicates that the Goldstone mode is
usually stable and the bivalent mode is always unstable. The linearized
equations for the second type of modes are coupled, they indicate which
modes will be excited when the orbit destabilizes. Numerical results for
the second class show that modes with a single eigenvalue are unstable
below a threshold amplitude. Conversely, modes with multiple eigenvalues
always seem unstable. This study could be applied to coupled mechanical
systems.
Filiaciones:
Caputo, J. G.:
INSA Rouen, Lab Math, F-76801 St Etienne Du Rouvray, France
Khames, I.:
INSA Rouen, Lab Math, F-76801 St Etienne Du Rouvray, France
Knippel, A.:
INSA Rouen, Lab Math, F-76801 St Etienne Du Rouvray, France
Panayotaros, P.:
Univ Nacl Autonoma Mexico, IIMAS, Dept Matemat & Mecan, Apdo Postal 20-126, Mexico City 01000, DF, Mexico
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