The hyperelliptic ζ-function and the integrable massive Thirring model

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

doi:10.1098/rspa.2002.1082

The hyperelliptic ζ-function and the integrable massive Thirring model

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

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	1581-1610
Number of pages	30
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	459
Issue number	2035
DOIs	https://doi.org/10.1098/rspa.2002.1082
Publication status	Published - 8 Jul 2003

Keywords

Hyperelliptic functions
Integrable systems
Massive Thirring model

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10.1098/rspa.2002.1082

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AU - Eilbeck, J. C.

AU - Enolskii, V. Z.

AU - Holden, H.

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Y1 - 2003/7/8

N2 - 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.

AB - 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.

KW - Hyperelliptic functions

KW - Integrable systems

KW - Massive Thirring model

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JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2035

ER -

The hyperelliptic ζ-function and the integrable massive Thirring model

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Keywords

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