@inproceedings{c23667ee366247ae93361523e7f378a3,

title = "Symmetric solutions of the dispersionless Toda hierarchy and associated conformal dynamics",

abstract = "Under certain reality conditions, a general solution to the dispersionless Toda lattice hierarchy describes deformations of simply-connected plane domains with a smooth boundary. The solution depends on an arbitrary (real positive) function of two variables which plays the role of a density or a conformal metric in the plane. We consider in detail the important class of symmetric solutions characterized by the density functions that depend only on the distance from the origin and that are positive and regular in an annulus r 01. We construct the dispersionless tau-function which gives formal local solution to the inverse potential problem and to the Riemann mapping problem and discuss the associated conformal dynamics related to viscous flows in the Hele-Shaw cell.",

keywords = "conformal maps, Dispersionless Toda hierarchy, Hele-Shaw flows, inverse potential problem",

author = "A. Zabrodin",

year = "2013",

doi = "10.1063/1.4828694",

language = "English",

isbn = "9780735411906",

series = "AIP Conference Proceedings",

pages = "203--222",

booktitle = "Nonlinear and Modern Mathematical Physics - Proceedings of the 2nd International Workshop",

note = "2nd International Workshop on Nonlinear and Modern Mathematical Physics, NMMP 2013 ; Conference date: 09-03-2013 Through 11-03-2013",

}