Lie algebraic noncommuting structures from reparametrization symmetry

Lie algebraic noncommuting structures from reparametrisation symmetry

We extend our earlier work of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. We show explicitly (in contrast to the earlier results in our paper [8]) that for some special choices of the reparametrisation parameter ǫ, one can obtain space-space noncommuting structures which are Lie-algebraic in for...

Lie symmetry analysis for Kawahara-KdV equations

We introduce a new solution for Kawahara-KdV equations. The Lie group analysis is used to carry out the integration of this equations. The similarity reductions and exact solutions are obtained based on the optimal system method.

Analytic reparametrization of semi-algebraic sets

Inmany problems in analysis, dynamics, and in their applications, it is important to subdivide objects under consideration into simple pieces, keeping control of high-order derivatives. It is known that semi-algebraic sets and mappings allow for such a controlled subdivision: this is the “Ck reparametrization theorem” which is a high-order quantitative version of the well-known results on the e...

Lie Algebraic Structures in Integrable Models, Affine Toda Field Theory

Constructing algebraic groups from their Lie algebras

A connected algebraic group in characteristic 0 is uniquely determined by its Lie algebra. In this paper an algorithm is given for constructing an algebraic group in characteristic 0, given its Lie algebra. Using this an algorithm is presented for finding a maximal reductive subgroup and the unipotent radical of an algebraic group.