M England and J C Eilbeck 2009 J. Phys. A: Math. Theor. 42 095210 doi:10.1088/1751-8113/42/9/095210
Abelian functions associated with a cyclic tetragonal curve of genus six
M England and J C Eilbeck
Show affiliationsWe develop the theory of Abelian functions defined using a tetragonal curve of genus six, discussing in detail the cyclic curve y4 = x5 + λ4x4 + λ3x3 + 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.
- PACS
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02.40.-k Geometry, differential geometry, and topology
02.30.Jr Partial differential equations
- MSC
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14H45 Special curves and curves of low genus
14H55 Riemann surfaces; Weierstrass points; gap sequences (See also 30Fxx)
- Subjects
- Dates
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Issue 9 (6 March 2009)
Received 30 October 2008, in final form 8 January 2009
Published 5 February 2009
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Abelian functions associated with a cyclic tetragonal curve of genus six
M England and J C Eilbeck 2009 J. Phys. A: Math. Theor. 42 095210
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