The hyperelliptic ζ-function and the integrable massive Thirring model

J. C. Eilbeck, V. Z. Enolskii, H. Holden

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


We provide a treatment of algebro-geometric solutions of the classical massive Thirring system in the framework of the Weierstrass-Klein theory of hyperelliptic functions. We show that the equations of this model generate the characteristic relations of hyperelliptic theory of even hyperelliptic curves, the same role that the Korteweg-de Vries (KdV) equation plays for odd hyperelliptic curves. We also consider the soliton limit of the solution obtained and derive the Kuznetsov-Mikhailov soliton as the limit.

Original languageEnglish
Pages (from-to)1581-1610
Number of pages30
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2035
Publication statusPublished - 8 Jul 2003


  • Hyperelliptic functions
  • Integrable systems
  • Massive Thirring model


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