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Nonlinear stability of oscillatory wave fronts in chains of coupled oscillators

A. carpio
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Abstract

We present a stability theory for kink propagation in chains of coupled oscillators and a new algorithm for the numerical study of kink dynamics. The numerical solutions are computed using an equivalent integral equation instead of a system of differential equations. This avoids uncertainty about the impact of artificial boundary conditions and discretization in time. Stability results also follow from the integral version. Stable kinks have a monotone leading edge and move with a velocity larger than a critical value which depends on the damping strength.

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A. carpio. 2004-04-26. Nonlinear stability of oscillatory wave fronts in chains of coupled oscillators. https://doi.org/10.1103/physreve.69.046601

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