Symmetric solutions of the dispersionless Toda hierarchy and associated conformal dynamics

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1 Citation (Scopus)

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 0<z<r1. 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.

Original languageEnglish
Title of host publicationNonlinear and Modern Mathematical Physics - Proceedings of the 2nd International Workshop
Pages203-222
Number of pages20
DOIs
Publication statusPublished - 2013
Externally publishedYes
Event2nd International Workshop on Nonlinear and Modern Mathematical Physics, NMMP 2013 - Tampa, FL, United States
Duration: 9 Mar 201311 Mar 2013

Publication series

NameAIP Conference Proceedings
Volume1562
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference2nd International Workshop on Nonlinear and Modern Mathematical Physics, NMMP 2013
Country/TerritoryUnited States
CityTampa, FL
Period9/03/1311/03/13

Keywords

  • conformal maps
  • Dispersionless Toda hierarchy
  • Hele-Shaw flows
  • inverse potential problem

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