منابع مشابه
Geometrization of the Lax Pair Tensors
The tensorial form of the Lax pair equations are given in a compact and geometrically transparent form in the presence of Cartan’s torsion tensor. Three dimensional spacetimes admitting Lax tensors are analyzed in detail. Solutions to Lax tensor equations include interesting examples as separable coordinates and the Toda lattice.
متن کاملLax pair tensors and integrable spacetimes
The use of Lax pair tensors as a unifying framework for Killing tensors of arbitrary rank is discussed. Some properties of the tensorial Lax pair formulation are stated. A mechanical system with a wellknown Lax representation – the three-particle open Toda lattice – is geometrized by a suitable canonical transformation. In this way the Toda lattice is realized as the geodesic system of a certai...
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The solution of the Lax tensor equations in the case Lαβγ = −Lβαγ was analyzed. The Lax tensors on the dual metrics were investigated. We classified all two dimensional metrics having the symmetric Lax tensor Lαβγ . The Lax tensors of the flat space, Rindler system and its dual were found.
متن کاملar X iv : g r - qc / 0 10 40 11 v 1 3 A pr 2 00 1 Geometrization of the Lax Pair Tensors
The tensorial form of the Lax pair equations are given in a compact and geometrically transparent form in the presence of Cartan's torsion ten-sor. Three dimensional spacetimes admitting Lax tensors are analyzed in detail. Solutions to Lax tensor equations include interesting examples as separable coordinates and the Toda lattice.
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— In this paper we give an algorithmic method of deriving the Lax pair for the modified Korteweg-de Vries hierarchy. For each n, the compatibility condition gives the n-th member of the hierarchy, rather than its derivative. A direct consequence of this is that we obtain the isomonodromy problem for the second Painlevé hierarchy, which is derived through a scaling reduction. Résumé (La paire de...
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ژورنال
عنوان ژورنال: Modern Physics Letters A
سال: 2000
ISSN: 0217-7323,1793-6632
DOI: 10.1142/s0217732300001924