2 4 Se p 20 02 On the Whitham Hierarchies : Reductions and Hodograph Solutions ∗
نویسندگان
چکیده
A general scheme for analyzing reductions of Whitham hierarchies is presented. It is based on a method for determining the S-function by means of a system of first order partial differential equations. Compatibility systems of differential equations characterizing both reductions and hodograph solutions of Whitham hierarchies are obtained. The method is illustrated by exhibiting solutions of integrable models such as the dispersionless Toda equation (heavenly equation) and the generalized Benney system.
منابع مشابه
0 40 40 05 v 2 2 9 A pr 2 00 4 Whitham hierarchy in growth problems ∗
We discuss the recently established equivalence between the Laplacian growth in the limit of zero surface tension and the universal Whitham hierarchy known in soliton theory. This equivalence allows one to distinguish a class of exact solutions to the Laplacian growth problem in the multiply-connected case. These solutions corerespond to finite-dimensional reductions of the Whitham hierarchy re...
متن کامل2 00 4 Whitham hierarchy in growth problems ∗
We discuss the recently established equivalence between the Laplacian growth in the limit of zero surface tension and the universal Whitham hierarchy known in soliton theory. This equivalence allows one to distinguish a class of exact solutions to the Laplacian growth problem in the multiply-connected case. These solutions corerespond to finite-dimensional reductions of the Whitham hierarchy re...
متن کامل2 M ay 2 00 4 S - functions , reductions and hodograph solutions of the r - th dispersionless modified KP and Dym hierarchies
We introduce an S-function formulation for the recently found r-th dispersionless modified KP and r-th dispersionless Dym hierarchies, giving also a connection of these S-functions with the Orlov functions of the hierarchies. Then, we discuss a reduction scheme for the hierarchies that together with the S-function formulation leads to hodograph systems for the associated solutions. We consider ...
متن کاملSe p 20 02 A hodograph transformation which applies to the heavenly equation ∗
A hodograph transformation for a wide family of multidimensional nonlinear partial differential equations is presented. It is used to derive solutions of the heavenly equation (dispersionless Toda equation) as well as a family of explicit ultra-hyperbolic selfdual vacuum spaces admiting only one Killing vector which is not selfdual, we also give the corresponding explicit Einstein–Weyl structures.
متن کاملSe p 20 06 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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003