10,760 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
Integrable Quasiclassical Deformations of Algebraic Curves
A general scheme for determining and studying integrable deformations of
algebraic curves is presented. The method is illustrated with the analysis of
the hyperelliptic case. An associated multi-Hamiltonian hierarchy of systems of
hydrodynamic type is characterized.Comment: 28 pages, no figure
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
Nonlinear Dynamics on the Plane and Integrable Hierarchies of Infinitesimal Deformations
A class of nonlinear problems on the plane, described by nonlinear
inhomogeneous -equations, is considered. It is shown that the
corresponding dynamics, generated by deformations of inhomogeneous terms
(sources) is described by Hamilton-Jacobi type equations associated with
hierarchies of dispersionless integrable systems. These hierarchies are
constructed by applying the quasiclassical -dressing method.Comment: 30 pages, tcilate
Hydrodynamic reductions and solutions of a universal hierarchy
The diagonal hydrodynamic reductions of a hierarchy of integrable
hydrodynamic chains are explicitly characterized. Their compatibility with
previously introduced reductions of differential type is analyzed and their
associated class of hodograph solutions is discussed.Comment: 19 page
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