Site menu:


This paper was originally published in Physica D. To download a preprint of this paper just click here.

This material is based upon work supported by the National Science Foundation under Grant Nos. DMS-0807653 and DMS-1206131. Any opinions, findings and conclusions or recomendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation (NSF).

Search box:

on this site:
on the web:

On the Stability Analysis of Periodic Sine-Gordon Traveling Waves

Christopher K. R. T. Jones, Robert Marangell, Peter D. Miller, and Ramón G. Plaza
Department of Mathematics, University of North Carolina, Chapel Hill
School of Mathematics and Statistics F07, University of Sydney
Department of Mathematics, University of Michigan, Ann Arbor
Departamento de Matemáticas y Mecánica, IIMAS-FENOMEC, Universidad Nacional Autónoma de México


We study the spectral stability properties of periodic traveling waves in the sine-Gordon equation, including waves of both subluminal and superluminal propagation velocities as well as waves of both librational and rotational types. We prove that only subluminal rotational waves are spectrally stable and establish exponential instability in the other three cases. Our proof corrects a frequently cited one given by Scott.