0 40 40 05 v 2 2 9 A pr 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
ar 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 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 کاملar X iv : g r - qc / 0 40 40 42 v 1 9 A pr 2 00 4 Vector field and rotational curves in dark galactic halos
We study equations of a non-gauge vector field in a spherically symmetric static metric. The constant vector field with a scale arrangement of components: the time component about the Planck mass m Pl and the radial component about M suppressed with respect to the Planck mass, serves as a source of metric reproducing flat rotation curves in dark halos of spiral galaxies, so that the velocity of...
متن کامل- qc / 0 40 40 42 v 2 2 5 A pr 2 00 4 Vector field and rotational curves in dark galactic halos
We study equations of a non-gauge vector field in a spherically symmetric static metric. The constant vector field with a scale arrangement of components: the temporal component about the Planck mass m Pl and the radial component about M suppressed with respect to the Planck mass, serves as a source of metric reproducing flat rotation curves in dark halos of spiral galaxies, so that the velocit...
متن کاملar X iv : g r - qc / 0 40 40 40 v 1 9 A pr 2 00 4 Could the Gravitons Have Rest Masses ?
If the cosmological constant Λ can not be neglected, we will show in this short report, that graviton should have a rest mass mg = √ 2Λ = √ 2Λh̄c−1 different from zero.
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