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Integrable equations of the dispersionless Hirota type and hypersurfaces in the Lagrangian Grassmannian
preprint
posted on 2007-05-23, 14:03 authored by Evgeny FerapontovEvgeny Ferapontov, Lenos Hadjikos, Karima KhusnutdinovaKarima KhusnutdinovaFamiliar examples include the Boyer-Finley equation uxx+uyy = eutt , the potential
form of the dispersionless Kadomtsev-Petviashvili (dKP) equation uxt−1
2u2
xx = uyy,
the dispersionless Hirota equation ( − )euxy + ( −
)euyt + (
− )eutx = 0, 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.
History
School
- Science
Department
- Mathematical Sciences
Publication date
2007Notes
This is a pre-print.Language
- en