Boris Kruglikov (UiT): Second order PDEs in 4D with half-flat conformal structure on every solution
Channel: Centrum Fizyki Teoretycznej PAN
Date: 2021-09-09

Boris Kruglikov (UiT).
Second order PDEs in 4D with half-flat conformal structure on every solution.
It was demonstrated previously that for classes of translationally invariant second order PDEs in 4D integrability is equivalent to the self-duality property of the conformal symbol. Here integrability is meant both in hydrodynamic sense and as the existence of a dispersionless Lax pair (dLp). In the general context hydrodynamic integrability is not developed, but we relate the existence of a dLp to half-flatness of the conformal symbol and to the Monge-Ampere property of the equation. We show several examples of integrable deformations of PDEs based on this. Joint work with S.Berjawi, E.Ferapotov, V.Novikov (Proc Royal Soc A 2020). 

GRIEG collaboration project: SCREAM workshop 2021.