Aspects of Solitons in Affine Integrable Hierarchies

Details Aspects of Solitons in Affine Integrable Hierarchies Aspects of Solitons in Affine Integrable Hierarchies

1997-01-10

arxiv.org/abs/solv-int/9701006v2

Physics

High Energy Physics

High Energy Physics - Theory

39 pages, LaTeX, Two talks presented by the authors at the ``International Workshop on Selected Topics of Theoretical and Mode

Scientific paper

We argue that one of the basic ingredients for the appearance of soliton solutions in integrable hierarchies, is the existence of ``vacuum solutions'' corresponding to Lax operators lying in some abelian subalgebra of the associated affine Kac-Moody algebra. Using the dressing transformation we construct the solutions in the orbit of those vacuum solutions, and conjecture that the solitons correspond to some special points in those orbits. The generalized tau-function for those hierarchies are defined for integrable highest weight representations. It applies for any level of the representation. We illustrate our methods with the recently proposed non abelian Toda models coupled to matter fields. A very special class of such theories possess a U(1) Noether charge that is proportional to a topological charge. That leads to a mechanism that confines the matter fields inside the solitons.

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