Abstract
We consider a very large class of hierarchies of zero-curvature equations constructed from affine Kac-Moody algebras Ĵ. We argue that one of the basic ingredients for the appearance of soliton solutions in such theories is the existence of “vacuum solutions” corresponding to Lax operators lying in some abelian (up to central term) subalgebra of Ĵ. Using the dressing transformation procedure we construct the solutions in the orbit of those vacuum solutions, and conjecture that the soliton solutions correspond to some special points in those orbits. The generalized tau-function for those hierarchies are defined for integrable highest weight representations of Ĵ, and it applies for any level of the representation and it is independent of its realization. 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, under a suitable gauge fixing of the conformal symmetry, is proportional to a topological charge. That leads to a mechanism that confines the matter fields inside the solitons.
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Ferreira, L.A., Guillén, J.S. (1998). Solitons and generalized tau-functions for affine integrable hierarchies. In: Aratyn, H., Imbo, T.D., Keung, WY., Sukhatme, U. (eds) Supersymmetry and Integrable Models. Lecture Notes in Physics, vol 502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105317
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DOI: https://doi.org/10.1007/BFb0105317
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