Volume 1, issue 1 (1997)

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Ward's solitons

Christopher Anand

Geometry & Topology 1 (1997) 9–20

arXiv: math.DG/9707234

Abstract

Using the ‘Riemann Problem with zeros’ method, Ward has constructed exact solutions to a (2 + 1)–dimensional integrable Chiral Model, which exhibit solitons with nontrivial scattering. We give a correspondence between what we conjecture to be all pure soliton solutions and certain holomorphic vector bundles on a compact surface.

Keywords
integrable system, chiral field, sigma model, soliton, monad, uniton, harmonic map
Mathematical Subject Classification
Secondary: 58F07
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Publication
Received: 4 December 1996
Revised: 16 May 1997
Published: 14 July 1997
Proposed: Simon Donaldson
Seconded: Frances Kirwan, Peter Kronheimer
Authors
Christopher Anand
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
16 Mill Lane
Cambridge
CB2 1SB
United Kingdom