The aim of the course is to give an introduction to the theory of integrable systems, both continuous and discrete. The characteristic feature of such systems is that they possess symmetries, conservation laws, and Bäcklund transformations, which allow one to construct for them interesting explicit solutions, including celebrated soliton solutions. Examples of such systems include well-known equations of mathematical physics such as the Korteweg-de Vries, nonlinear Schrödinger, Landau-Lifshitz equations.

Using algebraic and geometric methods, in this course we will study integrable nonlinear partial differential equations and discrete equations on lattices, which play essential roles in many branches of mathematics and physics, including algebra, geometry, combinatorics, numerical analysis, electromagnetism, fiber optics, and the theory of water waves.

these are scientific activities of the project
DISMA - Dipartimento di Eccellenza 2018-2022