## Abstract

It is known that the Korteweg-de Vries (KdV) equation is a geodesic flow of an L^{2} metric on the Bott-Virasoro group. This can also be interpreted as a flow on the space of projective connections on S^{1}. The space of differential operators Δ^{(n)}=∂^{n}+u_{2}∂ ^{n-2}+⋯+u_{n} form the space of extended or generalized projective connections. If a projective connection is factorizable Δ^{(n)}=(∂-((n+1)/2-1)p_{1}) ⋯(∂+(n-1)/2p_{n}) with respect to quasi primary fields p_{i}'s, then these fields satisfy ∑_{i=1}^{n}((n+1)/2-i)p_{i}=0. In this paper we discuss the factorization of projective connection in terms of affine connections. It is shown that the Burgers equation and derivative non-linear Schrödinger (DNLS) equation or the Kaup-Newell equation is the Euler-Arnold flow on the space of affine connections.

Original language | British English |
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Pages (from-to) | 231-242 |

Number of pages | 12 |

Journal | Journal of Geometry and Physics |

Volume | 46 |

Issue number | 3-4 |

DOIs | |

State | Published - Jun 2003 |

## Keywords

- Affine connections
- Integrable systems
- Projective connections

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