
Symmetry in Nonlinear Mathematical Physics  2009
Matthew England (HeriotWatt University, Edinburgh, UK)
Higher genus Abelian functions associated with algebraic curves
Abstract:
In recent years there has been a revival of interest in the theory of Abelian (multiply periodic) functions associated with algebraic curves. We can define such functions to generalise the classic Weierstrass pfunction and we seek to derive the related partial differential equations and addition formula.
After an introduction to the topic I will describe how we have generated new results for the functions associated to higher genus curves, giving examples for a cyclic tetragonal curve of genus six. I will discuss some of the key methods used to compute the results and demonstrate that such functions can give a solution to the KPequation.
Presentation

