Eur. Phys. J. B 19, 107-115 (2001)
https://doi.org/10.1007/s100510170355

Internal mode dynamics in driven nonlinear Klein-Gordon systems

¹ Grupo Interdisciplinar de Sistemas Complicados (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid, Edificio Sabatini, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
² Physikalisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany

Corresponding author: ^a anxo@math.uc3m.es

Received: 6 June 2000
Published online: 15 January 2001

Abstract

We study analytically and numerically the action of a constant force on the propagation of kinks in the and sine-Gordon systems, with and without dissipation. We specifically investigate the relation of the external force with the oscillations of the kink width due to excitation of its internal mode or quasimode. We demonstrate that both dc force and dissipation, either jointly or separately, damp the oscillations of the kink width. We further prove that, in contrast to earlier predictions, those oscillations can only arise if we use a distorted kink as initial condition for the evolution. Finally, we show that for the system the oscillations of the kink width come from the excitation of its internal mode, whereas in the sG equation they originate in the excitation of the lowest radiational modes and an internal mode induced by the discreteness of the numerical simulations.