Eugene Ferapontov (Loughborough University)
E.V.Ferapontov@lboro.ac.uk I will discuss integrable second order equations of the form
F(uxx, uxy, uyy, uxt, uyt, utt)=0
which constitute a single relation among second order partial derivatives of a function u(x, y, t). Familiar examples include the Boyer-Finley equation, the dispersionless Kadomtsev-Petviashvili equation, the dispersionless Hirota equation, etc. The integrability is understood as the existence of infinitely many hydrodynamic reductions. It will be demonstrated that the natural equivalence group of the problem is the symplectic group Sp(6), which reveals a remarkable correspondence between differential equations of the above type and hypersurfaces of the Lagrangian Grassmannian.