Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special section on Nonlinear Vibration in Mechanical Systems and Its Control-from Nano to Macro-
Reduced systems for Intrinsic Localized Modes on an infinite oscillator array
Daniel BrakeVakhtang Putkaradze
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2013 Volume 4 Issue 3 Pages 244-255


We reduce the complex mechanics of an Intrinsic Localized Mode (ILM) on an infinite monodirectional nonlinear coupled oscillator array. By using Hamiltonian Mechanics, we derive two systems - a simple case when only the position of the ILM is allowed to vary, and the more complex case where both position and amplitude are allowed to change with time. We arrive at a systems of nonlinear equations of motion. For the position-only system, the dynamics are determined solely by the level sets of the Hamiltonian. The four-variable system has a richer structure. We also analyze the effect of a defect, or an impurity, on the motion of the ILM within our framework.

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© 2013 The Institute of Electronics, Information and Communication Engineers
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