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Leur, Johan van de

doi:10.1155/s1073792801000290

Cited by 19 publications

(4 citation statements)

References 12 publications

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“…for the grading operator Q = λ d dλ + 1 2 α.H from (A.1). The term (−1) #(E (n) α ) corresponds to the mapping λ → −λ used in the case of the automorphism for the homogeneous gradation [21,1]. The numbers η Eα , η Fγ are eigenvalues in…”

Section: Step Operators and Twisted Automorphism Of Sl(2|1)mentioning

confidence: 99%

Supersymmetry and the KdV equations for integrable hierarchies with a half-integer gradation

2004

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Supersymmetry is formulated for integrable models based on the sl(2|1) loop algebra endowed with a principal gradation. The symmetry transformations which have half-integer grades generate supersymmetry. The sl(2|1) loop algebra leads to N = 2 supersymmetric mKdV and sinh-Gordon equations. The corresponding N = 1 mKdV and sinh-Gordon equations are obtained via reduction induced by twisted automorphism. Our method allows for a description of a non-local symmetry structure of supersymmetric integrable models.

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Section: Step Operators and Twisted Automorphism Of Sl(2|1)mentioning

confidence: 99%

Supersymmetry and the KdV equations for integrable hierarchies with a half-integer gradation

2004

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“…The loop group generalization of the automorphism in (4.18)-(4.19) has the following form [18] : σ (X(λ)) = (X(−λ)) T −1 ; X ∈ G = GL(m + 1) (4.25)…”

Section: Orthogonal Reduction Of the Gl(m + 1 C)-hierarchymentioning

confidence: 99%

“…The fixed points of the automorphism σ form a subgroup of G = GL(m + 1), called a twisted loop group of GL(m + 1). In reference [18], the twisted loop group of GL(n), in the context of n-component KP hierarchy, was used to find solutions of the Darboux-Egoroff system of PDE's.…”

Section: Orthogonal Reduction Of the Gl(m + 1 C)-hierarchymentioning

confidence: 99%

Integrable hierarchy for multidimensional Toda equations and topological–anti-topological fusion

Aratyn¹,

Gomes²,

Zímerman³

2003

Journal of Geometry and Physics

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The negative symmetry flows are incorporated into the Riemann-Hilbert problem for the homogeneous A m -hierarchy and its gl(m + 1, C) extension.A loop group automorphism of order two is used to define a sub-hierarchy of gl(m + 1, C) hierarchy containing only the odd symmetry flows. The positive and negative flows of the ±1 grade coincide with equations of the multidimensional Toda model and of topologicalanti-topological fusion.

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“…The next steps to take include elucidating the relationship among the nonlocal symmetries of (44) from corollary 6 and the symmetries found in [37] for the generalized (in the sense of [42]) WDVV equations. The relationship (if any exists) of the flows (52) to the flows (5.15) from [61] could be of interest too. Understanding the precise relationship of the symmetries from corollary 8 to the tau-function and the Bäcklund transformations for the WDVV equations from [4] is yet another challenge.…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

Infinite hierarchies of nonlocal symmetries of the Chen–Kontsevich–Schwarz type for the oriented associativity equations

Sergyeyev¹

2009

J. Phys. A: Math. Theor.

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We construct infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using solutions of associated vector and scalar spectral problems. The symmetries in question generalize those found by Chen, Kontsevich and Schwarz (Nucl. Phys. B 730 352–63) for the WDVV equations. As a byproduct, we obtain a Darboux-type transformation and a (conditional) Bäcklund transformation for the oriented associativity equations.

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Cited by 19 publications

References 12 publications

Supersymmetry and the KdV equations for integrable hierarchies with a half-integer gradation

Supersymmetry and the KdV equations for integrable hierarchies with a half-integer gradation

Integrable hierarchy for multidimensional Toda equations and topological–anti-topological fusion

Infinite hierarchies of nonlocal symmetries of the Chen–Kontsevich–Schwarz type for the oriented associativity equations

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