Integrable Dispersionless PDEs in 4D, Their Symmetry Pseudogroups and Deformations
Abstract
We study integrable non-degenerate Monge-Ampère equations of Hirota type in 4D and demonstrate that their symmetry algebras have a distinguished graded structure, uniquely determining those equations. This knowledge is used to deform these heavenly type equations into new integrable PDEs of the second-order with large symmetry pseudogroups. We classify the symmetric deformations obtained in this way and discuss self-dual hyper-Hermitian geometry of their solutions, thus encoding integrability via the twistor theory.
- Publication:
-
Letters in Mathematical Physics
- Pub Date:
- December 2015
- DOI:
- 10.1007/s11005-015-0800-z
- arXiv:
- arXiv:1410.7104
- Bibcode:
- 2015LMaPh.105.1703K
- Keywords:
-
- Mathematical Physics;
- Mathematics - Differential Geometry
- E-Print:
- This version is updated with an appendix about multi-component extensions of the integrable equations. Our deformations can be considered as reductions of such extensions (as they are reductions of the self-duality equation), but we stress that second order deformations carry the natural geometry which encodes integrability. We also expanded the introduction a bit