All Title Author
Keywords Abstract

Physics  2008 

Conformal weldings and Dispersionless Toda hierarchy

Full-Text   Cite this paper   Add to My Lib

Abstract:

Given a $C^1$ homeomorphism of the unit circle $\gamma$, let $f$ and $g$ be respectively the normalized conformal maps from the unit disc and its exterior so that $\gamma= g^{-1}\circ f$ on the unit circle. In this article, we show that by suitably defined time variables, the evolutions of the pairs $(g, f)$ and $(g^{-1}, f^{-1})$ can be described by an infinite set of nonlinear partial differential equations known as dispersionless Toda hierarchy. Relations to the integrable structure of conformal maps first studied by Wiegmann and Zabrodin \cite{WZ} are discussed. An extension of the hierarchy which contains both our solution and the solution of \cite{WZ} is defined.

Full-Text

comments powered by Disqus