Vojcak P. Coverings and nonlocal symmetries of Lax-integrable PDEs (abstract)

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Speaker: Petr Vojčák

Title: Coverings and nonlocal symmetries of Lax-integrable PDEs

We consider four three-dimensional Lax-integrable equations: (1) the rdDym equation u_{ty}=u_xu_{xy}-u_yu_{xx}, (2) the Pavlov equation u_{yy}=u_{tx}+u_yu_{xx}-u_xu_{xy}, (3) the universal hierarchy equation u_{yy}=u_tu_{xy}-u_yu_{tx}, and (4) the modified Veronese web equation u_{ty}=u_tu_{xy}-u_yu_{tx}.

For each equation, expanding the known Lax pairs in formal series in the spectral parameter, we construct two differential coverings and completely describe the nonlocal symmetry algebras associated with these coverings. For all four pairs of coverings, the obtained Lie algebras of symmetries manifest similar (but not identical) structures; they are (semi)direct sums of the Witt algebra, the algebra of vector fields on the line, and loop algebras, all of which contain a component of finite grading. We also discuss actions of recursion operators on shadows of nonlocal symmetries.

This is the joint work with Hynek Baran, Iosif S. Krasil'shchik and Oleg I. Morozov.

Slides: VojcakTrieste2018slides.pdf

Event: Local and Nonlocal Geometry of PDEs and Integrability, 8-12 October 2018, SISSA, Trieste, Italy.
The conference in honor of Joseph Krasil'shchik's 70th birthday.