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The geometry of real sine-Gordon wavetrains

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, 43210, Columbus, OH, USA

    Nicholas M. Ercolani & M. Gregory Forest

Authors
  1. Nicholas M. Ercolani
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  2. M. Gregory Forest
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Additional information

Communicated by S.-T. Yau

Supported in part by NSF Grant No. MCS-8202288

Supported in part by NSF Grant No. MCS-8002969

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Ercolani, N.M., Forest, M.G. The geometry of real sine-Gordon wavetrains. Commun.Math. Phys. 99, 1–49 (1985). https://doi.org/10.1007/BF01466592

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  • DOI: https://doi.org/10.1007/BF01466592

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