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By Nagnibida N. I.

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The Au (0: Schlesinger equations (5) as functions of xo, xl, ... , X n • (41) 0, ... J. Hitchin in Oxford in June 1992. J. C. Advanced Fellowship. J. A. 1991, "Solitons, nonlinear evolution equations and inverse scattering," LMS Lecture Note Series, 149, Cambridge University Press, Cambridge. Hitchin, N. , Lindstrom, U. and Rocek, M. 1987, Commun. Math. , 108, 537-589. Jimbo, M. and Miwa, T. 1981, Physica, 2D, 407-448. J. 1993, this volume, pp9-16. J. J. 1992, "Self-duality and the Painleve transcendents", to be published.

4>: this gives X=l. To get X_ = (\}I(O)g\}l(O)-l)_ it can be shown (cf. [8]) that the thing to do is to use a natural homomorphism L from the abelian group generated by w(O) onto the Jacobi variety of X, so that for each k we have a 1-parameter family L(tkZk) of line bundles over X of degree zero. Then X depends only upon (tj, z when [( Xij) ::: [0 ® L( al + zk a2 ) for some fixed [0 with the variables Xij and tk identified as earlier. We may think of this as a family ofline bundles over X which vary linearly over its Jacobi variety.

ZAKRZEWSKI Department of Mathematical Sciences The University Durham DIlJ 3LE UK ABSTRACT. We study extended structure solutions of the 52 sigma model and the corresponding Skyrme models in (2 + 1) dimensions. We review some results reported earlier and concentrate our attention on the process of annihilation of two such structures - one corresponding to a soliton like object and another to an antisoliton. We find that the process of annihilation proceeds in three stages; the initial approach, then rapid annihilation of the soliton cores followed slow annihilation of the soliton tails.

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