XXXIX Workshop on Geometric Methods in Physics 28.06-4.07.2020
IX School on Geometry and Physics 22-26.06.2020

Raffaele Vitolo

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.

  1. Partial differential equations as submanifolds of jet spaces. The contact distributions. Generalized symmetries of PDEs.
  2. Conservation laws of PDEs and their characteristic vectors.
  3. Hamiltonian PDEs: Poisson brackets and hierarchies of commuting integrals.

Event sponsored by:
of Bialystok
University of Bialystok

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