Site menu:


This paper has been published in Memoirs of the AMS. To download a preprint of this paper just click here.

This material is based upon work supported by the National Science Foundation under Grant No. DMS-0807653. 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:

The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates

Robert J. Buckingham and Peter D. Miller
Department of Mathematical Sciences, University of Cincinnati
Department of Mathematics, University of Michigan, Ann Arbor


We study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also high-frequency librational motion in the tails. We show that for small times independent of the semiclassical scaling parameter, both types of motion are accurately described by explicit formulae involving elliptic functions. These formulae demonstrate consistency with predictions of Whitham's formal modulation theory in both the hyperbolic (modulationally stable) and elliptic (modulationally unstable) cases.