Hydrodynamic reductions of multi-dimensional dispersionless PDEs : the test for integrability

@inproceedings{Ferapontov1989HydrodynamicRO,
  title={Hydrodynamic reductions of multi-dimensional dispersionless PDEs : the test for integrability},
  author={E. V. Ferapontov and K R Khusnutdinova},
  year={1989}
}
A (d + 1)-dimensional dispersionless PDE is said to be integrable if its ncomponent hydrodynamic reductions are locally parametrized by (d − 1)n arbitrary functions of one variable. The most important examples include the fourdimensional heavenly equation descriptive of self-dual Ricci-flat metrics and its sixdimensional generalization arising in the context of sdiff(Σ2) self-dual Yang-Mills equations. Given a multi-dimensional PDE which does not pass the integrability test, the method of… CONTINUE READING
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