Communications in Mathematical Physics

, Volume 99, Issue 1, pp 1–49

The geometry of real sine-Gordon wavetrains


  • Nicholas M. Ercolani
    • Department of MathematicsThe Ohio State University
  • M. Gregory Forest
    • Department of MathematicsThe Ohio State University

DOI: 10.1007/BF01466592

Cite this article as:
Ercolani, N.M. & Forest, M.G. Commun.Math. Phys. (1985) 99: 1. doi:10.1007/BF01466592


The characterization ofreal, N phase, quasiperiodic solutions of the sine-Gordon equation has been an open problem. In this paper we achieve this result, employing techniques of classical algebraic geometry which have not previously been exploited in the soliton literature. A significant by-product of this approach is a naturalalgebraic representation of the full complex isospectral manifolds, and an understanding of how the real isospectral manifolds are embedded. By placing the problem in this general context, these methods apply directly to all soliton equations whose multiphase solutions are related to hyperelliptic functions.

Copyright information

© Springer-Verlag 1985