Finite-gap integration of the SU(2) Bogomolny equations
H.W. Braden, V.Z. Enolski
TL;DR
This paper develops an algebro-geometric method to solve the Weyl equation associated with SU(2) magnetic monopoles, providing a new approach to finite-gap integration within the ADHMN construction.
Contribution
It introduces a direct algebro-geometric solution to the Weyl equation using Baker-Akhiezer functions, bypassing the need to solve Nahm's equation.
Findings
Explicit solutions for the Weyl equation are obtained.
The method offers a new perspective on finite-gap integration for monopoles.
The approach simplifies the construction of magnetic monopoles in SU(2).
Abstract
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 means. The (adjoint) Weyl equation is solved using an ans\"atz of Nahm in terms of Baker-Akhiezer functions. The solution of Nahm's equation is not directly used in our development.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Mathematical Physics Problems · Numerical methods for differential equations