ترغب بنشر مسار تعليمي؟ اضغط هنا

Affine Weyl group approach to Painleve equations

103   0   0.0 ( 0 )
 نشر من قبل Masatoshi Noumi
 تاريخ النشر 2003
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Masatoshi Noumi




اسأل ChatGPT حول البحث

An overview is given on recent developments in the affine Weyl group approach to Painleve equations and discrete Painleve equations, based on the joint work with Y. Yamada and K. Kajiwara.



قيم البحث

اقرأ أيضاً

179 - Yasuhiko Yamada 2010
An explicit form of the Lax pair for the q-difference Painleve equation with affine Weyl group symmetry of type E^{(1)}_8 is obtained. Its degeneration to E^{(1)}_7, E^{(1)}_6 and D^{(1)}_5 cases are also given.
Eigenvalue problems for linear differential equations, such as time-independent Schrodinger equations, can be generalized to eigenvalue problems for nonlinear differential equations. In the nonlinear context a separatrix plays the role of an eigenfun ction and the initial conditions that give rise to the separatrix play the role of eigenvalues. Previously studied examples of nonlinear differential equations that possess discrete eigenvalue spectra are the first-order equation $y(x)=cos[pi xy(x)]$ and the first, second, and fourth Painleve transcendents. It is shown here that the differential equations for the first and second Painleve transcendents can be generalized to large classes of nonlinear differential equations, all of which have discrete eigenvalue spectra. The large-eigenvalue behavior is studied in detail, both analytically and numerically, and remarkable new features, such as hyperfine splitting of eigenvalues, are described quantitatively.
The affine Weyl groups with their corresponding four types of orbit functions are considered. Two independent admissible shifts, which preserve the symmetries of the weight and the dual weight lattices, are classified. Finite subsets of the shifted w eight and the shifted dual weight lattices, which serve as a sampling grid and a set of labels of the orbit functions, respectively, are introduced. The complete sets of discretely orthogonal orbit functions over the sampling grids are found and the corresponding discrete Fourier transforms are formulated. The eight standard one-dimensional discrete cosine and sine transforms form special cases of the presented transforms.
We utilize group-theoretical methods to develop a matrix representation of differential operators that act on tensors of any rank. In particular, we concentrate on the matrix formulation of the curl operator. A self-adjoint matrix of the curl operato r is constructed and its action is extended to a complex plane. This scheme allows us to obtain properties, similar to those of the traditional curl operator.
139 - S. Albeverio , S.V. Kozyrev 2008
The general construction of frames of p-adic wavelets is described. We consider the orbit of a mean zero generic locally constant function with compact support (mean zero test function) with respect to the action of the p-adic affine group and show t hat this orbit is a uniform tight frame. We discuss relation of this result to the multiresolution wavelet analysis.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا