Journal of Differential Geometry

Dispersionless integrable systems in 3D and Einstein-Weyl geometry

Eugene V. Ferapontov and Boris S. Kruglikov

Full-text: Open access

Abstract

For several classes of second-order dispersionless PDEs, we show that the symbols of their formal linearizations define conformal structures that 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.

Article information

Source
J. Differential Geom., Volume 97, Number 2 (2014), 215-254.

Dates
First available in Project Euclid: 15 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1405447805

Digital Object Identifier
doi:10.4310/jdg/1405447805

Mathematical Reviews number (MathSciNet)
MR3263506

Zentralblatt MATH identifier
1306.37084

Citation

Ferapontov, Eugene V.; Kruglikov, Boris S. Dispersionless integrable systems in 3D and Einstein-Weyl geometry. J. Differential Geom. 97 (2014), no. 2, 215--254. doi:10.4310/jdg/1405447805. https://projecteuclid.org/euclid.jdg/1405447805


Export citation