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On the WDVV equations in five-dimensional gauge theories
It is well-known that the perturbative prepotentials of four-dimensional ${\cal N}=2$ supersymmetric Yang-Mills theories satisfy the generalized WDVV equations, regardless of the gauge group. In thisExpand
Prolongation structure of the Landau-Lifshitz equation
The prolongation method of Wahlquist and Estabrook is applied to the Landau–Lifshitz equation. The resulting prolongation algebra is shown to be isomorphic to a subalgebra of the tensor product ofExpand
Prolongation structure of the Krichever–Novikov equation
We completely describe Wahlquist-Estabrook prolongation structures (coverings) dependent on $u,\,u_x,\,u_{xx},\,u_{xxx}$ for the Krichever-Novikov equationExpand
Trigonometric Solutions of the WDVV Equations from Root Systems
By introduction of an additional variable and addition of a Weyl invariant correction term to the perturbative prepotential in five-dimensional Seiberg-Witten theory we construct solutions of theExpand
Prolongation structure of the KdV equation in the bilinear form of Hirota
The prolongation structure of the KdV equation in the bilinear form of Hirota is determined, the resulting Lie algebra is realised and the Backlund transformation obtained from the prolongationExpand
The harmonic map and Killing fields for self-dual SU(3) Yang-Mills equations
Using symbolic computations, the unique metric in the space of fields, required to describe self-dual SU(3) Yang-Mills equations by a harmonic map, is determined. Moreover the complete Lie algebra ofExpand
Symbolic computations in applied differential geometry
The main aim of this paper is to contribute to the automatic calculations in differential geometry and its applications, with emphasis on the prolongation theory of Estabrook and Wahlquist, and theExpand
Quantization of differential calculi on universal enveloping algebras
A method to construct differential calculi on quantized universal enveloping algebras is discussed. These differential calculi are obtained by quantizing calculi on 'classical' enveloping algebrasExpand