7,942 research outputs found
Exact Solutions of Integrable 2D Contour Dynamics
A class of exact solutions of the dispersionless Toda hierarchy constrained
by a string equation is obtained. These solutions represent deformations of
analytic curves with a finite number of nonzero harmonic moments. The
corresponding tau-functions are determined and the emergence of cusps is
studied.Comment: 13 pages, 3 figure
-regularity of the -adic valuation of the Fibonacci sequence
We show that the -adic valuation of the sequence of Fibonacci numbers is a
-regular sequence for every prime . For , we determine that
the rank of this sequence is , where is the
restricted period length of the Fibonacci sequence modulo .Comment: 7 pages; publication versio
Genus-zero Whitham hierarchies in conformal-map dynamics
A scheme for solving quasiclassical string equations is developped to prove
that genus-zero Whitham 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.Comment: 12 pages, 3 figure
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