dorsal/arxiv
View SchemaAspects of Solitons in Affine Integrable Hierarchies
| Authors | Luiz A. Ferreira, Joaquin Sanchez Guillen |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9701006 |
| URL | https://arxiv.org/abs/solv-int/9701006 |
Abstract
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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"abstract": "We argue that one of the basic ingredients for the appearance of soliton\nsolutions in integrable hierarchies, is the existence of ``vacuum solutions\u0027\u0027\ncorresponding to Lax operators lying in some abelian subalgebra of the\nassociated affine Kac-Moody algebra. Using the dressing transformation we\nconstruct the solutions in the orbit of those vacuum solutions, and conjecture\nthat the solitons correspond to some special points in those orbits. The\ngeneralized tau-function for those hierarchies are defined for integrable\nhighest weight representations. It applies for any level of the representation.\nWe illustrate our methods with the recently proposed non abelian Toda models\ncoupled to matter fields. A very special class of such theories possess a U(1)\nNoether charge that is proportional to a topological charge. That leads to a\nmechanism that confines the matter fields inside the solitons.",
"arxiv_id": "solv-int/9701006",
"authors": [
"Luiz A. Ferreira",
"Joaquin Sanchez Guillen"
],
"categories": [
"solv-int",
"hep-th",
"nlin.SI"
],
"title": "Aspects of Solitons in Affine Integrable Hierarchies",
"url": "https://arxiv.org/abs/solv-int/9701006"
},
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