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Integrable Hierarchies, Solitons and Infinite Dimensional Algebras

Abstract

This project aims the study of the structure of a class of nonlinear equations constructed in terms of an affine algebraic structure and a zero curvature representation.The algebraic methods employed are systematic and sufficiently general for the construction of a series of equations of motion, dubbed hierarchy, its soliton solutions and the corresponding Backlund transformations.Such framework are used in the description of integrable defects describing the interpolation between two soliton solutions.The quantized version of discretized integrable models and its relationship between the quantum analogue of Backlund transformations is also part of this investigation.The study of open spin chains associated to twisted affine algebras is another subject interest.This project constitutes an extension of the research being developed by the group of IFT-Unesp along the past decades. (AU)

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