On the central quadric ansatz: integrable models and Painlevé reductions

@article{Ferapontov2012OnTC,
  title={On the central quadric ansatz: integrable models and Painlev{\'e} reductions},
  author={Eugene V. Ferapontov and Benoit Huard and Alex Zhongyi Zhang},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2012},
  volume={45}
}
It was observed by Tod (1995 Class. Quantum Grav.12 1535–47) and later by Dunajski and Tod (2002 Phys. Lett. A 303 253–64) that the Boyer–Finley (BF) and the dispersionless Kadomtsev–Petviashvili (dKP) equations possess solutions whose level surfaces are central quadrics in the space of independent variables (the so-called central quadric ansatz). It was demonstrated that generic solutions of this type are described by Painlevé equations PIII and PII, respectively. The aim of our paper is… 

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