Abelian functions associated with a cyclic tetragonal curve of genus six

England, M. and Eilbeck, J.C. (2009) Abelian functions associated with a cyclic tetragonal curve of genus six. Journal of Physics A: Mathematical and Theoretical, 42(9), 095210. (doi: 10.1088/1751-8113/42/9/095210)

Abstract

We develop the theory of Abelian functions defined using a tetragonal curve of genus six, discussing in detail the cyclic curve y^4 = x^5 + λ[4]x^4 + λ[3]x^3 + λ[2]x^2 + λ[1]x + λ[0]. We construct Abelian functions using the multivariate sigma-function associated with the curve, generalizing the theory of theWeierstrass℘-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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: England, Dr Matthew
• Authors: England, M., and Eilbeck, J.C.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Physics A: Mathematical and Theoretical
• Journal Abbr.: J. Phys. A: Math. Theor.
• Publisher: Institute of Physics
• ISSN: 1751-8113
• ISSN (Online): 1751-8121
• Published Online: 05 February 2009
• Copyright Holders: Copyright © 2009 Institute of Physics
• First Published: First published in Journal of Physics A: Mathematical and Theoretical 42(9):095210
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher