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Ward’s Solitons II: Exact Solutions

Published online by Cambridge University Press:  20 November 2018

Christopher Kumar Anand
Christopher Kumar Anand*
Affiliation:
Département de Mathématiques, Université de Bretagne Occidentale, 6, avenue le Gorgeu, B.P. 452, 29275 Brest, France email: [email protected]
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Abstract

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In a previous paper, we gave a correspondence between certain exact solutions to a (2 + 1)-dimensional integrable Chiral Model and holomorphic bundles on a compact surface. In this paper, we use algebraic geometry to derive a closed-form expression for those solutions and show by way of examples how the algebraic data which parametrise the solution space dictates the behaviour of the solutions.

Résumé

Résumé

Dans un article précédent, nous avons démontré que les solutions d’un modèle chiral intégrable en dimension (2 + 1) correspondent aux fibrés vectoriels holomorphes sur une surface compacte. Ici, nous employons la géométrie algébrique dans une construction explicite des solutions. Nous donnons une formule matricielle et illustrons avec trois exemples la signification des invariants algébriques pour le comportement physique des solutions.

Keywords

35Q51integrable systemchiral fieldsigma modelsolitonmonadunitonharmonic map
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 6 , 01 December 1998 , pp. 1119 - 1137
Copyright
Copyright © Canadian Mathematical Society 1998

References

[An95] Anand, C.K., Uniton Bundles. Comm. Anal. Geom. 3(1995), 371–419.Google Scholar
[An97] Anand, C.K., Ward's Solitons. Geom. Topol. 1(1997), 9–20. http://www.maths.warwick.ac.uk/gt/GTVol1/paper2.abs.html Google Scholar
[An98] Anand, C.K., A closed form for unitons. J. Math. Soc. Japan (to appear). http://gauss.univ-brest.fr/anand Google Scholar
[Do] Donaldson, S.K., Instantons and Geometric Invariant Theory. Comm.Math. Phys. 93(1984), 453–460.Google Scholar
[Hi] Hitchin, N.J., Monopoles and Geodesics. Comm.Math. Phys. 83(1982), 579–602.Google Scholar
[Hu] Hurtubise, J.C., Instantons and Jumping Lines. Comm.Math. Phys. 105(1986), 107–122.Google Scholar
[Io] Ioannidou, T., Soliton Solutions and Nontrivial Scattering in an Integrable Chiral Model in (2 + 1) Dimensions. J. Math. Phys. 37(1996), 3422.ndash;3441.Google Scholar
[OSS] Okonek, C., Schneider, M. and Spindler, H., Vector bundles on complex projective spaces. Birkhauser, Boston, 1980.Google Scholar
[Su] Sutcliffe, P.M., Nontrivial soliton scattering in an integrable chiral model in (2+1)-dimensions. J. Math. Phys. 33(1992), 2269.ndash;2278.Google Scholar
[Wa90] Ward, R.S., Classical Solutions of the Chiral Model, Unitons, and Holomorphic Vector Bundles. Commun. Math. Phys. 123(1990), 319–332.Google Scholar
[Wa95] Ward, R.S., Nontrivial scattering of localised solitons in a (2 + 1)-dimensional integrable system. Phys. Lett. A 208(1995), 203–208.Google Scholar