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Integrable dispersionless PDEs in 4D, their symmetry pseudogroups and deformations. (English) Zbl 1378.17046
Summary: 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.

17B80 Applications of Lie algebras and superalgebras to integrable systems
37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
17B65 Infinite-dimensional Lie (super)algebras
17B70 Graded Lie (super)algebras
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