Nonlinear stability of oscillatory wave fronts in chains of coupled oscillators.
We present a stability theory for kink propagation in chains of coupled oscillators and a different 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.
Carpio
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Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain. ana_carpio@mat.ucm.es