TY - JOUR
T1 - Abelian functions associated with a cyclic tetragonal curve of genus six
AU - England, M.
AU - Eilbeck, J. C.
PY - 2009
Y1 - 2009
N2 - We develop the theory of Abelian functions defined using a tetragonal curve of genus six, discussing in detail the cyclic curve y4 = x 5 + ?4x4 + ?3x 3 + ?2x2 + ?1x + ?0. We construct Abelian functions using the multivariate s-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 s(u) and a new addition formula. © 2009 IOP Publishing Ltd.
AB - We develop the theory of Abelian functions defined using a tetragonal curve of genus six, discussing in detail the cyclic curve y4 = x 5 + ?4x4 + ?3x 3 + ?2x2 + ?1x + ?0. We construct Abelian functions using the multivariate s-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 s(u) and a new addition formula. © 2009 IOP Publishing Ltd.
UR - http://www.scopus.com/inward/record.url?scp=67651021466&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/42/9/095210
DO - 10.1088/1751-8113/42/9/095210
M3 - Article
SN - 1751-8113
VL - 42
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 9
M1 - 095210
ER -