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Infinite Algebras, Solitons and Integrable Defects

Grant number: 22/13584-0
Support Opportunities:Scholarships in Brazil - Doctorate
Effective date (Start): April 01, 2023
Effective date (End): March 31, 2027
Field of knowledge:Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
Principal Investigator:José Francisco Gomes
Grantee:Ysla França Adans
Host Institution: Instituto de Física Teórica (IFT). Universidade Estadual Paulista (UNESP). Campus de São Paulo. São Paulo , SP, Brazil

Abstract

This project aims to study a class of non-linear (integrable) equations constructed in terms of an affine algebraic structure and the so called zero curvature representation. The algebraic methods used are systematic and sufficiently general for the construction of a series of time evolution equations named hierarchy, their soliton solutions and the so called Backlund transformations. These are employed in the formalism of integrable defects that describe the interpolation of two soliton solutions. As a natural extension, this project aims to give continuity to study the construction of quasi-periodic solutions of integrable models. Furthermore, we intend to extend the results already obtained in the context of classical integrability to the quantum context.

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