### Abstract

Using methods of geometry and cohomology developed recently, we study the Monge-Ampère equation, arising as the first nontrivial equation in the associativity equations, or WDVV equations. We describe Hamiltonian and symplectic structures as well as recursion operators for this equation in its orginal form, thus treating the independent variables on an equal footing. Besides this we present nonlocal symmetries and generating functions (cosymmetries).

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 2004 |

### Publication series

Name | |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1727 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-35Q53
- MSC-37K05
- EWI-3547
- Hamiltonian structure
- Monge-Ampère equation
- IR-65911
- Recursion operator
- associativity equations
- conservation law
- symplectic structure
- Symmetry

## Cite this

Kersten, P. H. M., Krasil'shchik, I., & Verbovetsky, A. V. (2004).

*The Monge-Ampère equation: Hamiltonian and symplectic structures, recursions, and hierarchies*. Enschede: University of Twente, Department of Applied Mathematics.