Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · solv-int/9704002

Extended matrix Gelfand-Dickey hierarchies: reduction to classical Lie algebras

Laszlo Feher·Ian Marshall
View original source ↗Read source document ↗Export metadata ↓

Abstract

The Drinfeld-Sokolov reduction method has been used to associate with $gl_n$ extensions of the matrix r-KdV system. Reductions of these systems to the fixed point sets of involutive Poisson maps, implementing reduction of $gl_n$ to classical Lie algebras of type $B, C, D$, are here presented. Modifications corresponding, in the first place to factorisation of the Lax operator, and then to Wakimoto realisations of the current algebra components of the factorisation, are also described.

Explore related subjects

solv-inthep-thnlin.SI

Keep this discovery

BibTeXRIS

Laszlo Feher, Ian Marshall. 1997-03-31. Extended matrix Gelfand-Dickey hierarchies: reduction to classical Lie algebras. https://doi.org/10.1088/0305-4470%2F30%2F16%2F022

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2013

On two aspects of the Painleve analysis

We use the Calogero equation to illustrate the following two aspects of the Painleve analysis of nonlinear PDEs. First, if a nonlinear equation passes the Painleve test for integrability, the singular expansions of its solutions around characteristic hypersurfaces can be neither single-valued functions of independent variables nor single-valued functionals of data. Second, if the truncation of singular expansions of solutions is consistent, the truncation not necessarily leads to the simplest, or elementary, auto-Backlund transformation related to the Lax pair.

solv-int↗
arXiv2009

The tetrahedral analog of Veneziano amplitude

In solv-int/9812016 it was shown that the Veneziano amplitude in string theory comes naturally from one of the simplest solutions of the functional pentagon equation (FPE). More generally, FPE is intimately connected with the duality condition for scattering processes. Here I find the amplitude that comes the same way from a solution of the functional tetrahedron equation, with the duality replaced by the local Yang - Baxter equation.

solv-int↗
arXiv2004

Equations of Geodesic Deviation and the Inverse Scattering Transform

Solutions of equations of geodesic deviation in three- and four- dimensional spaces obtained by the inverse scattering transform are considered. It is shown that in the case of three-dimensional space solutions of geodesic deviation equations are reduced to solutions of the well-known Zakharov-Shabat problem. In four- dimensional space system of geodesic deviation equations is associated with $3\times 3$ matrix Schrödinger equation, and dependence on parameters defined by the nonlinear equations of three-wave interaction.

solv-int↗