On N = 4 Integrable Models

Saidi, E. H.; Sedra, M. B.

doi:10.1142/s0217751x94000406

Cited by 9 publications

(5 citation statements)

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“…In this section, we consider the Lie supersymmeries associated with fermionic degrees of freedom. These symmetries have been explored in many context in physics and can be thought as a possible extension of the one discussed in the previous section [16,17,18,19]. In fact, we expect that Lie supersymmeries can be used to engineer a new class of materials.…”

Section: Lie Supersymmetries and Doping Materials Geometriesmentioning

confidence: 94%

Lie symmetries and 2D Material Physics

Belhaj¹,

Sedra²

2014

Preprint

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Inspired from Lie symmetry classification, we establish a correspondence between rank two Lie symmetries and 2D materials physics. The material unit cell is accordingly interpreted as the geometry of a root system. The hexagonal cells, appearing in graphene like models, are analyzed in some details and are found to be associated with A 2 and G 2 Lie symmetries. This approach can be applied to Lie supersymmetries associated with fermionic degrees of freedom. It has been suggested that these extended symmetries can offer a new way to deal with doping material geometries. Motivated by Lie symmetry applications in high energy physics, we speculate on a possible connection with (p, q) brane networks used in the string theory compactification on singular Calabi-Yau manifolds.

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Section: Lie Supersymmetries and Doping Materials Geometriesmentioning

confidence: 94%

Lie symmetries and 2D Material Physics

Belhaj¹,

Sedra²

2014

Preprint

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“…To begin, we remark that Ξ (p,q) m is the space of differential operators whose elements d (p,q) m (u) are the generalization of the well-known scalar Lax operator involved in the analysis of the so-called KdV hierarchies and in Toda theories [15,16,17]. The simplest example is given by the Hill operator…”

Section: The ξ (Pq) M Spacementioning

confidence: 99%

Pseudo-Differential Operators and Integrable Models

Sedra

2009

Preprint

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The importance of the theory of pseudo-differential operators in the study of non linear integrable systems is point out. Principally, the algebra Ξ of nonlinear (local and nonlocal) differential operators, acting on the ring of analytic functions u s (x, t), is studied. It is shown in particular that this space splits into several classes of subalgebras Σ jr , j = 0, ±1, r = ±1 completely specified by the quantum numbers: s and (p, q) describing respectively the conformal weight (or spin) and the lowest and highest degrees. The algebra Σ ++ (and its dual Σ −− ) of local (pure nonlocal) differential operators is important in the sense that it gives rise to the explicit form of the second hamiltonian structure of the KdV system and that we call also the Gelfand-Dickey Poisson bracket. This is explicitly done in several previous studies, see for the moment [4,5,14]. Some results concerning the KdV and Boussinesq hierarchies are derived explicitly.

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“…KdV integrable hierarchy systems, describing non linear phenomena, are associated to non linear differential equations that can be solved exactly [1,2,3,4]. The subject of nonlinear phenomena play an important role in many areas of sciences more notably in applied mathematics and physics.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of KdV equation

Akdi¹,

Sedra²

2013

astp

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It is by now well known that the 2d-non-linear KdV differential equation u + u + uu = 0 is one of the most popular and famous equations of mathematical physics. The major content of the recent work deals with the establishing of a numerical schemes, based on the finite difference, to descretize this famous equation. The latter, in it self, is not the principal focus of our work. It's exact solvability (the existence of an explicit analytic solution) is behind our motivation to develop a numerical strong approach to be tested first on this famous equation before used it for other models. The principal result of the this work is the presentation of a proof for the unconditional stability of our schemes. Other important properties are presented.

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On N = 4 Integrable Models

Cited by 9 publications

References 0 publications

Lie symmetries and 2D Material Physics

Lie symmetries and 2D Material Physics

Pseudo-Differential Operators and Integrable Models

Numerical simulation of KdV equation

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