Integrable Equations of the Dispersionless Hirota type and Hypersurfaces in the Lagrangian Grassmannian

@article{Ferapontov2007IntegrableEO,
  title={Integrable Equations of the Dispersionless Hirota type and Hypersurfaces in the Lagrangian Grassmannian},
  author={E. Ferapontov and L. Hadjikos and K. Khusnutdinova},
  journal={International Mathematics Research Notices},
  year={2007},
  volume={2010},
  pages={496-535}
}
We investigate integrable second-order equations of the formwhich typically arise as the Hirota-type relations for various (2 + 1)-dimensional dispersionless hierarchies. Familiar examples include the Boyer-Finley equation , the potential form of the dispersionless Kadomtsev-Petviashvili (dKP) equation , the dispersionless Hirota equation , etc. The integrability is understood as the existence of an infinity of hydrodynamic reductions. We demonstrate that the natural equivalence group of the… Expand
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