The geometry of real sine-Gordon wavetrains

Nicholas M Ercolani, M. Gregory Forest

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

The characterization of real, 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 natural algebraic 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.

Original languageEnglish (US)
Pages (from-to)1-49
Number of pages49
JournalCommunications in Mathematical Physics
Volume99
Issue number1
DOIs
StatePublished - Mar 1985
Externally publishedYes

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Soliton Equation
Quasi-periodic Solutions
Sine-Gordon Equation
Algebraic Geometry
Complex Manifolds
Solitons
Open Problems
solitary waves
geometry
Context

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

The geometry of real sine-Gordon wavetrains. / Ercolani, Nicholas M; Forest, M. Gregory.

In: Communications in Mathematical Physics, Vol. 99, No. 1, 03.1985, p. 1-49.

Research output: Contribution to journalArticle

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