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.
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - 2009|