Genus-zero Whitham hierarchies in conformal-map dynamics

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Elsevier Science BV
Google Scholar
Research Projects
Organizational Units
Journal Issue
A scheme for solving quasiclassical-string equations is developed to prove that genus-zero hitham hierarchies describe the deformations of planar domains determined by rational conformal-maps. This property is applied in normal matrix models to show that deformations of simply-connected supports of eigenvalues under changes of coupling constants are governed by genus-zero Whitham hierarchies.
©2006 Elsevier B.V. Partially supported by MEC project FIS2005-00319
Unesco subjects
[1] M.Z. Bazant, D. Crowdy, Conformal mapping methods for interfacial dynamics, in: S. Yip (Ed.), Handbook of Materials Modeling, vol. 1, Springer, 2005. [2] P.Ya. Polubarinova-Kochina, Dokl. Acad. Nauk SSSR 47 (1945) 254. [3] P.P. Kufarev, Dokl. Acad. Nauk SSSR 75 (1950) 507. [4] S. Richardson, J. Fluid Mech. 56 (1972) 609. [5] P.W. Wiegmann, P.B. Zabrodin, Commun. Math. Phys. 213 (2000) 523. [6] M. Mineev-Weinstein, P. Wiegmann, A. Zabrodin, Phys. Rev. Lett. 84 (2000) 5106. [7] I. Krichever, M. Mineev-Weinstein, P. Wiegmann, A. Zabrodin, Physica D 198 (2004) 1. [8] A. Zabrodin, Teor. Mat. Fiz. 142 (2005) 197. [9] D. Crowdy, Quadrature domains and fluid dynamics, in: Operator Theory: Advances and Applications, in: A Harold Shapiro Anniversary, vol. 156, Birkhäuser, 2005, p. 113. [10] H.S. Shapiro, The Schwarz Functions and its Generalization to Higher Dimensions, Wiley, New York, 1992. [11] I.M. Krichever, Commun. Pure Appl. Math. 47 (1994) 437. [12] K. Takasaki, Dispersionless integrable hierarchies revisited, Conference on Riemann–Hilbert Problems, Integrability and Asymptotics, RHPIA/talks/takasaki.pdf, SISSA, Trieste, 2005. [13] L. Martínez Alonso, E. Medina, Phys. Lett. B 610 (2005) 277. [14] R. Teodorescu, E. Bettelheim, O. Agam, A. Zabrodin, P. Wiegmann, Nucl. Phys. B 700 (2004) 521; R. Teodorescu, E. Bettelheim, O. Agam, A. Zabrodin, P. Wiegmann, Nucl. Phys. B 704 (2005) 407. [15] D. Bensimon, L.P. Kadanoff, S. Liang, B.I. Shraiman, C. Tang, Rev. Mod. Phys. 58 (1986) 977.