Abstract
We provide a pedagogical introduction to some aspects of integrability, dualities and deformations of physical systems in [Formula: see text] and in [Formula: see text] dimensions. In particular, we concentrate on the T-duality of point particles and strings as well as on the Ruijsenaars duality of finite many-body integrable models, we review the concept of the integrability and, in particular, of the Lax integrability and we analyze the basic examples of the Yang–Baxter deformations of nonlinear [Formula: see text]-models. The central mathematical structure which we describe in detail is the [Formula: see text]-model which is the dynamical system exhibiting all those three phenomena simultaneously. The last part of the paper contains original results, in particular, a formulation of sufficient conditions for strong integrability of non-degenerate [Formula: see text]-models.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
