J. C. Eilbeck,1 V. Z. Enolski,2 S. Matsutani,3 Y. Ônishi4 and E. Previato5 1Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS… (More)

Expressions for the periods of first- and second-kind integrals on hyperelliptic curves are given in terms of theta-constants. They are derived with the help of Thomae's classical formulae and… (More)

We develop the Ercolani-Sinha construction of SU (2) monopoles and make this effective for (a five parameter family of centred) charge 3 monopoles. In particular we show how to solve the… (More)

We give an elementary and rigorous proof of the Thomae type formula for the singular curves µ N = m j=1 (λ − λ 2j) N−1 m j=0 (λ − λ 2j+1). To derive the Thomae formula we use the traditional… (More)

A comprehensive algebro-geometric integration of the two component Nonlinear Vector Schrödinger equation (Manakov system) is developed. The allied spectral variety is a trigonal Rie-mann surface,… (More)

A computer-algebra aided method is carried out, for determining geometric objects associated to differential operators that satisfy the elliptic ansatz. This results in examples of Lamé curves with… (More)

We develop the theory of generalized Weierstrass σ and ℘ functions defined on a trigonal curve of genus three. The specific example of the “purely trigonal”curve y = x +λ3x 3 +λ2x 2 +λ1x+λ0 is… (More)

We are solving the classical Riemann-Hilbert problem of rank N > 1 on the extended complex plane punctured in 2m + 2 points, for N × N quasi-permutation monodromy matrices with 2m(N − 1) parameters.… (More)

We are solving the classical Riemann-Hilbert problem of rank N > 1 on the extended complex plane punctured in 2m + 2 points, for N × N quasi-permutation monodromy matrices. Our approach is based on… (More)

The ADHMN construction of magnetic monopoles is given in terms of the (normalizable) solutions of an associated Weyl equation. We focus here on solving this equation directly by algebro-geometric… (More)