61 citations · 693 across the 58 of their papers we have counts for
4 papers · 1 filter
Building Abelian Functions with Generalised Baker-Hirota Operators
Matthew England, Chris Athorne
We present a new systematic method to construct Abelian functions on Jacobian varieties of plane, algebraic curves. The main tool used is a symmetric generalisation of the bilinear…
Generalised Elliptic Functions
Matthew England, Chris Athorne
We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise the…
Deriving bases for Abelian functions
Matthew England
We present a new method to explicitly define Abelian functions associated with algebraic curves, for the purpose of finding bases for the relevant vector spaces of such functions.…
A genus six cyclic tetragonal reduction of the Benney equations
Matthew England, John Gibbons
A reduction of Benney's equations is constructed corresponding to Schwartz-Christoffel maps associated with a family of genus six cyclic tetragonal curves. The mapping function, a…