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Geometrization of the Lax Pair Tensors
, 2001
"... 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 co ..."
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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
On the Lax pairs of the sixth Painlevé equation
, 2006
"... The dependence of the sixth equation of Painlevé on its four parameters (2α, −2β, 2γ,1 − 2δ) = (θ 2 ∞, θ 2 0, θ 2 1, θ 2 x) is holomorphic, therefore one expects all its Lax pairs to display such a dependence. This is indeed the case of the second order scalar “Lax” pair of Fuchs, but the second or ..."
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The dependence of the sixth equation of Painlevé on its four parameters (2α, −2β, 2γ,1 − 2δ) = (θ 2 ∞, θ 2 0, θ 2 1, θ 2 x) is holomorphic, therefore one expects all its Lax pairs to display such a dependence. This is indeed the case of the second order scalar “Lax” pair of Fuchs, but the second
DISCRETE LAX PAIRS, REDUCTIONS AND HIERARCHIES
, 2008
"... The term ‘Lax pair’ refers to linear systems (of various types) that are related to nonlinear equations through a compatibility condition. If a nonlinear equation possesses a Lax pair, then the Lax pair may be used to gather information about the behaviour of the solutions to the nonlinear equation. ..."
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Cited by 3 (0 self)
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The term ‘Lax pair’ refers to linear systems (of various types) that are related to nonlinear equations through a compatibility condition. If a nonlinear equation possesses a Lax pair, then the Lax pair may be used to gather information about the behaviour of the solutions to the nonlinear equation
V.: The Lax pairs for the Holt system
 J. Phys. A
, 1999
"... By using known noncanonical transformation between the Holt system and the HenonHeiles system the Lax pairs for all the integrable cases of the Holt system are constructed from the known Lax representations for the HenonHeiles system. ..."
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Cited by 2 (0 self)
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By using known noncanonical transformation between the Holt system and the HenonHeiles system the Lax pairs for all the integrable cases of the Holt system are constructed from the known Lax representations for the HenonHeiles system.
FEYNMAN DIAGRAMS AND LAX PAIR EQUATIONS
"... Abstract. We find a Lax pair equation corresponding to the ConnesKreimer Birkhoff factorization of the character group of a Hopf algebra. This flow preserves the locality of counterterms. In particular, we obtain a flow for the character given by Feynman rules, and relate this flow to the Renormali ..."
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Abstract. We find a Lax pair equation corresponding to the ConnesKreimer Birkhoff factorization of the character group of a Hopf algebra. This flow preserves the locality of counterterms. In particular, we obtain a flow for the character given by Feynman rules, and relate this flow
Lax pair tensors and integrable spacetimes
, 1997
"... grqc/9707003 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 threeparticle open Toda lattice – is geometrized by a ..."
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grqc/9707003 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 threeparticle open Toda lattice – is geometrized
Lax pair tensors in arbitrary dimensions
, 1998
"... Abstract. A recipe is presented for obtaining Lax tensors for any ndimensional Hamiltonian system admitting a Lax representation of dimension n. Our approach is to use the Jacobi geometry and couplingconstant metamorphosis to obtain a geometric Lax formulation. We also exploit the results to const ..."
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to construct integrable spacetimes, satisfying the weak energy condition. Short title: Lax pair tensors
Weak Lax pairs for lattice equations
, 2011
"... We consider various 2D lattice equations and their integrability, from the point of view of 3D consistency, Lax pairs and Bäcklund transformations. We show that these concepts, which are associated with integrability, are not strictly equivalent. In the course of our analysis, we introduce a number ..."
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We consider various 2D lattice equations and their integrability, from the point of view of 3D consistency, Lax pairs and Bäcklund transformations. We show that these concepts, which are associated with integrability, are not strictly equivalent. In the course of our analysis, we introduce a
Lax pairs and Darboux transformations for Euler equations
 Studies in Appl. Math
"... In this article, we will report the recent developments on Lax pairs and Darboux transformations for Euler equations of inviscid fluids. ..."
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Cited by 9 (8 self)
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In this article, we will report the recent developments on Lax pairs and Darboux transformations for Euler equations of inviscid fluids.
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