2 00 4 Whitham hierarchy in growth problems ∗
نویسنده
چکیده
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 representable as equations of hydrodynamic type which are solvable by means of the generalized hodograph method.
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 کاملar X iv : 0 81 0 . 24 27 v 3 [ m at h - ph ] 2 1 A pr 2 00 9 The multicomponent 2 D Toda hierarchy : dispersionless limit Manuel Mañas and Luis Mart́ınez
The factorization problem of the multi-component 2D Toda hierarchy is used to analyze the dispersionless limit of this hierarchy. A dispersive version of the Whitham hierarchy defined in terms of scalar Lax and Orlov–Schulman operators is introduced and the corresponding additional symmetries and string equations are discussed. Then, it is shown how KP and Toda pictures of the dispersionless Wh...
متن کامل00 1 ∂ - equations , integrable deformations of quasiconformal mappings and Whitham hierarchy ∗
∂-equations, integrable deformations of quasiconformal mappings and Whitham hierarchy * B. Konopelchenko Abstract It is shown that the dispersionless scalar integrable hierarchies and, in general, the universal Whitham hierarchy are nothing but classes of integrable deformations of quasiconformal mappings on the plane. Examples of deformations of quasiconformal mappings associated with explicit...
متن کاملar X iv : h ep - t h / 02 09 08 5 v 2 7 O ct 2 00 2 Matrix models vs . Seiberg – Witten / Whitham theories
We discuss the relation between matrix models and the Seiberg–Witten type (SW) theories, recently proposed by Dijkgraaf and Vafa. In particular, we prove that the partition function of the Hermitean one-matrix model in the planar (large N) limit coincides with the prepotential of the corresponding SW theory. This partition function is the logarithm of a Whitham τ-function. The corresponding Whi...
متن کاملThe twistor theory of Whitham hierarchy
We have generalized the approach in of Dunajski, Mason and Tod [10] and established a 1-1 correspondence between a solution of the universal Whitham hierarchy [23] and a twistor space. The twistor space consists of a complex surface and a family of complex curves together with a meromorphic 2-form. The solution of the Whitham hierarchy is given by deforming the curve in the surface. By treating...
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 2005