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 prolongation structure is derived. The results are compared with those found by Wahlquist and Estabrook (1975) and by Hirota (1980)

Hierarchical index sets in algebraic modelling languages

Multi-dimensional algebraic modelling languages make extensive use of simple and compound index sets. In this paper the multi-dimensional modelling paradigm is extended with the concept of a hierarchical index set to support the use of hierarchical data structures. The appropriate reference and indexing mechanisms are introduced, together with mechanisms to support various set operations. Special attention is paid to the Cartesian product of two hierarchical index sets. The modelling of multi-stage programming models is supported through the introduction of a hierarchical indexing mechanism. The extensions proposed in this paper are compared to existing facilities designed to support the modelling of hierarchical structures

Prolongation structures for supersymmetric equations

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 the KdV equation of Manin-Radul. Using the theory of Kac-Moody Lie superalgebras, the explicit form of the resulting Lie superalgebra is determined. It is shown to be isomorphic to RMR*Cov+(C(2), sigma ), where RMR is an eight-dimensional radical. An auto-Backlund transformation is derived from the prolongation structure and the relationship with known solution methods of the SKdV equation is analysed. In addition it is indicated how a super-position principle for the SKdV equation can be obtaine

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 of the Lie algebra so(3) with the elliptic curve v α 2−v β 2=j β−j α (α,β=1,2,3), which is essentially a subalgebra of the Lie algebra applied by Date et al. in a different context. Taking a matrix representation of so(3) gives rise to a Lax pair of the Landau–Lifshitz equation in agreement with the results found by Sklyanin. A system of related equations is deduced which can be used for the computation of auto‐Bäcklund transformations of the Landau–Lifshitz equation

Prolongation structures for supersymmetric equations

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 the KdV equation of Manin-Radul. Using the theory of Kac-Moody Lie superalgebras, the explicit form of the resulting Lie superalgebra is determined. It is shown to be isomorphic to RMR*Cov+(C(2), sigma ), where RMR is an eight-dimensional radical. An auto-Backlund transformation is derived from the prolongation structure and the relationship with known solution methods of the SKdV equation is analysed. In addition it is indicated how a super-position principle for the SKdV equation can be obtaine

A bi-Hamiltonian supersymmetric geodesic equation

A supersymmetric extension of the Hunter-Saxton equation is constructed. We present its bi-Hamiltonian structure and show that it arises geometrically as a geodesic equation on the space of superdiffeomorphisms of the circle that leave a point fixed endowed with a right-invariant metric.Comment: 9 pages, no figure

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 prolongation structure is derived. The results are compared with those found by Wahlquist and Estabrook (1975) and by Hirota (1980)

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Product placement is een goed alternatief voor televisiecommercials. Consumenten waarderen product placement beter en ze vertonen nauwelijks reclamevermijdend gedrag. En: consumenten blijken geadverteerde merken goed te onthouden, zo blijkt uit onderzoek van de Radboud Universiteit Nijmegen in samenwerking met De Vos & Jansen Marktonderzoek