# Dispersionless integrable systems in 3D and Einstein-Weyl geometry

@article{Ferapontov2012DispersionlessIS, title={Dispersionless integrable systems in 3D and Einstein-Weyl geometry}, author={Eugene V. Ferapontov and Boris S. Kruglikov}, journal={arXiv: Mathematical Physics}, year={2012} }

For several classes of second order dispersionless PDEs, we show that the symbols of their formal linearizations define conformal structures which must be Einstein-Weyl in 3D (or self-dual in 4D) if and only if the PDE is integrable by the method of hydrodynamic reductions. This demonstrates that the integrability of these dispersionless PDEs can be seen from the geometry of their formal linearizations.

## 72 Citations

### Dispersionless integrable systems and the Bogomolny equations on an Einstein–Weyl geometry background

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### Integrable Dispersionless PDEs in 4D, Their Symmetry Pseudogroups and Deformations

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- 2015

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- 2018

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- 2014

Abstract We exploit the correspondence between the three–dimensional Lorentzian Einstein–Weyl geometries of the hyper–CR type and the Veronese webs to show that the former structures are locally…

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### Dispersionless (3+1)-dimensional integrable hierarchies

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- 2017

A multi-dimensional version of the R-matrix approach to the construction of integrable hierarchies of (3+1)-dimensional dispersionless systems of the type recently introduced in Sergyeyev.

### Characteristic integrals in 3D and linear degeneracy

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- 2021

Conservation laws vanishing along characteristic directions of a given system of PDEs are known as characteristic conservation laws, or characteristic integrals. In 2D, they play an important role in…

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