503 research outputs found
Integrable equations of the dispersionless Hirota type and hypersurfaces in the Lagrangian Grassmannian
We investigate integrable second order equations of the form
F(u_{xx}, u_{xy}, u_{yy}, u_{xt}, u_{yt}, u_{tt})=0.
Familiar examples include the Boyer-Finley equation, the potential form of
the dispersionless Kadomtsev-Petviashvili equation, the dispersionless Hirota
equation, etc. The integrability is understood as the existence of infinitely
many hydrodynamic reductions. We demonstrate that the natural equivalence group
of the problem is isomorphic to Sp(6), revealing a remarkable correspondence
between differential equations of the above type and hypersurfaces of the
Lagrangian Grassmannian. We prove that the moduli space of integrable equations
of the dispersionless Hirota type is 21-dimensional, and the action of the
equivalence group Sp(6) on the moduli space has an open orbit.Comment: 32 page
Systems of conservation laws with third-order Hamiltonian structures
We investigate -component systems of conservation laws that possess
third-order Hamiltonian structures of differential-geometric type. The
classification of such systems is reduced to the projective classification of
linear congruences of lines in satisfying additional
geometric constraints. Algebraically, the problem can be reformulated as
follows: for a vector space of dimension , classify -tuples of
skew-symmetric 2-forms such that for some non-degenerate symmetric
.Comment: 31 page
Singer quadrangles
[no abstract available
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