|XXXIX Workshop on Geometric Methods in Physics||28.06-4.07.2020|
|IX School on Geometry and Physics||22-26.06.2020|
Introduction to the geometry of PDEs and integrable systems
The lectures are an introduction to the theory of symmetries and conservation laws for PDEs and their application to integrable systems. Integrable systems are systems of PDEs for which it is possible to construct large classes of solutions. In geometric terms, PDEs for which it is possible to construct infinite sequences ('hierarchies') of symmetries or conservation laws that commute with respect to certain bracket operations are usually integrable. We will focus on the bi-Hamiltonian construction of hierarchies of conserved quantities.
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