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.
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Giovanni Manno