Integrable dispersionless PDE in 4D, their symmetry pseudogroups and deformations

TL;DR

This paper investigates integrable 4D dispersionless PDEs, revealing their symmetry structures, deforming them into new integrable equations, and exploring their geometric properties through twistor theory.

Contribution

It introduces a classification of symmetry-preserving deformations of 4D integrable PDEs and links their geometric structures to twistor theory.

Findings

Symmetry algebras have a unique graded structure.

Deformations lead to new integrable PDEs with large symmetry groups.

Solutions exhibit self-dual hyper-Hermitian geometry.

Abstract

We study integrable non-degenerate Monge-Ampere equations of Hirota type in 4D and demonstrate that their symmetry algebras have a distinguished graded structure, uniquely determining the equations. This is used to deform these heavenly type equations into new integrable PDE of the second order with large symmetry pseudogroups. We classify the obtained symmetric deformations and discuss self-dual hyper-Hermitian geometry of their solutions, which encode integrability via the twistor theory.