Projective and affine connections on S1 and integrable systems

✍ Scribed by Partha Guha

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 92 KB
• Volume: 46
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(02)00053-0

✦ Synopsis

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

with respect to quasi primary fields p i 's, then these fields satisfy n i=1 ((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.