1 - 10 of 21 articles
LetΠ: E → M be a fiber bundle and let Γ be an infinitesimal Lie transformation group acting onE. We announce various new results concerning the cohomology of the Γ invariant variational bicomplex (Ω
(J∞(E)), dH, dV) and the associated Γ invariant Euler-Lagrange complex. As one application...
Factors of a given system of PDEs are solutions of an adjoint system of PDEs related to the system's Fréchet derivative. In this paper, we introduce the notion of potential conservation laws, arising from specific types of factors, which lead to useful potential systems. Point symmetries of a...
A method for computing symmetries and conservation laws of integro-differential equations is proposed. It resides in reducing an integro-differential equation to a system of boundary differential equations and in computing symmetries and conservation laws of this system. A geometry of boundary...
There exists an (
) + 1 parameter quantum group deformation of GLn which has been constructed independently by several (groups of) authors. In this note, I give an explicitR-matrix for this multiparameter family. This gives additional information on the nature of this family and facilitates...
In this paper, we present several instances where infinite-dimensional flag varieties and their holomorphic line bundles play a role in integrable systems. As such, we give the correspondence between flag varieties and Darboux transformations for the KP hierarchy and the nth KdV hierarchy. We...
In this paper, we introduce a package to compute homology and cohomology spaces of Lie superalgebras. We describe most of its features and the implementation in REDUCE.
In this paper, we announce several new results concerning the cohomology of the variational bicomplex for a second-order scalar hyperbolic equation in the plane. These cohomology groups are represented by the conservation laws, and certain form-valued generalizations, for the equation. Our...
The groups E
∞) of Vinogradov'sC-spectral sequence for determined systems of evolution equations are considered. Presentation of these groups useful in practical computations is obtained. The group E
∞) is calculated for a system of Schrödinger type equations.
We show that to any Poisson manifold and, more generally, to any triangular Lie bialgebroid in the sense of Mackenzie and Xu, there correspond two differential Gerstenhaber algebras in duality, one of which is canonically equipped with an operator generating the graded Lie algebra bracket, i.e....
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