## Abstract

Using diffeomorphism group vector fields on C-multiplied tori and the related Lie-algebraic structures, we study multi-dimensional dispersionless integrable systems that describe conformal structure generating equations of mathematical physics. An interesting modification of the devised Lie-algebraic approach subject to spatial-dimensional invariance and meromorphicity of the related differential-geometric structures is described and applied in proving complete integrability of some conformal structure generating equations. As examples, we analyze the Einstein–Weyl metric equation, the modified Einstein–Weyl metric equation, the Dunajski heavenly equation system, the first and second conformal structure generating equations and the inverse first Shabat reduction heavenly equation. We also analyze the modified Plebański heavenly equations, the Husain heavenly equation and the general Monge equation along with their multi-dimensional generalizations. In addition, we construct superconformal analogs of the Whitham heavenly equation.

Original language | English (US) |
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Article number | 079 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 15 |

DOIs | |

State | Published - 2019 |

## All Science Journal Classification (ASJC) codes

- Analysis
- Mathematical Physics
- Geometry and Topology

## Keywords

- Casimir invariants
- Conformal structures
- Hamiltonian system
- Lax
- Lax integrability
- Lie
- Lie-algebraic scheme
- Loop Lie algebra
- Multi-dimensional heavenly equations
- Multi-dimensional integrable heavenly equations
- Poisson structure
- R-structure
- Sato equations
- Torus diffeomorphisms