# The explicit form of the Lie algebra of Wahlquist and Estabrook. A presentation problem

@inproceedings{Eck1983TheEF, title={The explicit form of the Lie algebra of Wahlquist and Estabrook. A presentation problem}, author={H. N. van Eck}, year={1983} }

The structure of the KdV-Lie algebra of Wahlquist and Estabrook is made explicit. This is done with help of a table of Lie-products and an inherent grading of the algebra.

#### 17 Citations

Lie algebra computations

- Mathematics
- 1989

In the context of prolongation theory, introduced by Wahlquist and Estabrook, computations of a lot of Jacobi identities in (infinite-dimensional) Lie algebras are necessary. These computations can… Expand

A non-Archimedean approach to prolongation theory

- Mathematics
- 1986

Some evolution equations possess infinite-dimensional prolongation Lie algebras which can be made finite-dimensional by using a bigger (non-Archimedean) field. The advantage of this is that… Expand

Lie algebras responsible for zero-curvature representations of scalar evolution equations

- Mathematics, Physics
- Journal of Geometry and Physics
- 2019

Zero-curvature representations (ZCRs) are well known to be one of the main tools in the theory of integrable PDEs. In particular, Lax pairs for (1+1)-dimensional PDEs can be interpreted as ZCRs.

Some Local Properties of Bäcklund Transformations

- Mathematics
- 1998

For Bäcklund transformations, treated as relations in the categoryof diffieties, local conditions of effectivity and normality are introduced,having implications for the solution generating… Expand

Prolongation structures for supersymmetric equations

- Mathematics
- 1990

The well known prolongation technique of Wahlquist and Estabrook (1975) for nonlinear evolution equations is generalized for supersymmetric equations and applied to the supersymmetric extension of… Expand

Coverings and Fundamental Algebras for Partial Differential Equations

Following I. S. Krasilshchik and A. M. Vinogradov [8], we regard PDEs as infinite-dimensional manifolds with involutive distributions and consider their special mor-phisms called differential… Expand

Coverings and the Fundamental Group for Kdv Type Equations

- 2003

Following A.M. Vinogradov and I.S. Krasilshchik, we regard systems of PDEs as manifolds with integrable distributions and consider their special morphisms called differential coverings, which include… Expand

Coverings and the Fundamental Group for Partial Differential Equations

- 2004

Following I. S. Krasilshchik and A. M. Vinogradov [8], we regard PDEs as infinite-dimensional manifolds with involutive distributions and consider their special mor-phisms called differential… Expand

Infinite‐dimensional Estabrook–Wahlquist prolongations for the sine‐Gordon equation

- Mathematics, Physics
- 1995

We are looking for the universal covering algebra for all symmetries of a given partial differential equation (PDE), using the sine‐Gordon equation as a typical example for a nonevolution equation.… Expand

HIGHER JET PROLONGATION LIE ALGEBRAS AND B ¨ ACKLUND TRANSFORMATIONS FOR (1 + 1)-DIMENSIONAL PDES

- Mathematics, Physics
- 2013

For any (1+1)-dimensional (multicomponent) evolution PDE, we define a sequence of Lie algebras $F^p$, $p=0,1,2,3,...$, which are responsible for all Lax pairs and zero-curvature representations… Expand

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