Abelian functions associated with a cyclic tetragonal curve of genus six

M. England; J. C. Eilbeck

doi:10.1088/1751-8113/42/9/095210

Abelian functions associated with a cyclic tetragonal curve of genus six

M. England, J. C. Eilbeck

Heriot-Watt University

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18 Citations (Scopus)

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Abstract

We develop the theory of Abelian functions defined using a tetragonal curve of genus six, discussing in detail the cyclic curve y⁴ = x ⁵ + λ₄x⁴ + λ₃x ³ + λ₂x² + λ₁x + λ₀. We construct Abelian functions using the multivariate σ-function associated with the curve, generalizing the theory of the Weierstrass -function. We demonstrate that such functions can give a solution to the KP-equation, outlining how a general class of solutions could be generated using a wider class of curves. We also present the associated partial differential equations satisfied by the functions, the solution of the Jacobi inversion problem, a power series expansion for σ(u) and a new addition formula.

Original language	English
Article number	095210
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	42
Issue number	9
DOIs	https://doi.org/10.1088/1751-8113/42/9/095210
Publication status	Published - 2009
Externally published	Yes

Bibliographical note

This is an author-created, un-copyedited version of an article accepted
for publication in Journal of Physics A: Mathematical and Theoretical. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/1751-8113/42/9/095210

ASJC Scopus subject areas

Mathematical Physics
General Physics and Astronomy
Statistical and Nonlinear Physics
Modelling and Simulation
Statistics and Probability

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Cite this

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abstract = "We develop the theory of Abelian functions defined using a tetragonal curve of genus six, discussing in detail the cyclic curve y4 = x 5 + λ4x4 + λ3x 3 + λ2x2 + λ1x + λ0. We construct Abelian functions using the multivariate σ-function associated with the curve, generalizing the theory of the Weierstrass -function. We demonstrate that such functions can give a solution to the KP-equation, outlining how a general class of solutions could be generated using a wider class of curves. We also present the associated partial differential equations satisfied by the functions, the solution of the Jacobi inversion problem, a power series expansion for σ(u) and a new addition formula.",

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Abelian functions associated with a cyclic tetragonal curve of genus six

Abstract

Bibliographical note

ASJC Scopus subject areas

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