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Integrable Models, Solitons and their Symmetries

Abstract

Integrable models have become an important tool in understanding the non-perturbative aspects of physical theories. They may be useful in testing confinement schemes, quantum theory of solitons, etc. In many cases they provide realistic models for important phenomena in solid state, statistical mechanics as well as in high energy physics under some suitable conditions. Integrable hierarchies as the Korteweg-de-Vries (KdV) and the Kadomtzev-Petviashvili (KP) have important applications in hidrodynamics and other phenomena in non linear physics. Recently, high technology in telecommunications is making use of solitons propagating in fiber optics described by the non linear Schroedinger hierarchy. More recently, integrable models have played an important role in describing the coupling constant for effective Yang-Mills low energy actions in four dimensions. Non perturbative aspects of field theories describing the fundamental interactions in nature are in general related to soliton solutions (instantons or monopoles) and to a nontrivial vacuum structure. Soliton solutions are localized solutions of non linear equations scattering elastically and preserving its original shape and velocity. This amazing fact may be explained by the numerous conservation laws that characterize integrable models. Our research within the past 12 years is based on the application of Lie algebraic methods to the study of integrable hierarchies and may be classified in 2 main topics: the formulation and the Lie algebraic structure of integrable model. Within this topic, we have proposed a 2-loop algebraic structure from which the Conformal Affine Toda models (CAT) were constructed. Its... (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
FERREIRA‚ LA; GUILLÉN‚ J.S. Infinite symmetries in the Skyrme model. Physics Letters B, v. 504, n. 1, p. 195-200, 2001.

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