Dispersionless fermionic KdV

Barcelos-Neto, J.; Constandache, A.; Das, Ashok

doi:10.1016/s0375-9601(00)00189-4

Cited by 17 publications

(34 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A number of supersymmetric extensions have been formulated for both classical and quantum mechanical systems. In particular, such supersymmetric generalizations have been constructed for hydrodynamic-type systems (e.g., the Korteweg-de Vries equation [2,3], the Sawada-Kotera equation [4], polytropic gas dynamics [5,6] and a Gaussian irrotational compressible fluid [7]) as well as other nonlinear wave equations, e.g., the Schrödinger equation [8] and the sine/sinh-Gordon equation [9][10][11]. Parameterizations of strings and Nambu-Goto membranes have been used to supersymmetrize the Chaplygin gas in (1 + 1) and (2 + 1) dimensions respectively [12].…”

Section: Introductionmentioning

confidence: 99%

Algebraic Aspects of the Supersymmetric Minimal Surface Equation

Grundland

Hariton

2017

Symmetry

View full text Add to dashboard Cite

Abstract:In this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. A classification of the one-dimensional subalgebras is performed, which results in a list of 143 conjugacy classes with respect to action by the supergroup generated by the Lie superalgebra. The symmetry reduction method is used to obtain invariant solutions of the supersymmetric minimal surface equation. The classical minimal surface equation is also examined and its group-theoretical properties are compared with those of the supersymmetric version.

show abstract

Section: Introductionmentioning

confidence: 99%

Algebraic Aspects of the Supersymmetric Minimal Surface Equation

Grundland

Hariton

2017

Symmetry

View full text Add to dashboard Cite

show abstract

“…As shown in [2] that finding the dispersionless limit of the Kupershmidt equation is bit tricky. If one tries scaling ∂ → ǫ∂ then one runs automatically in trouble since ∂ −1 toǫ −1 ∂ would diverge in the limit ǫ → 0.…”

Section: Construction Of Dispersionless Kuper-kdv Equation Via Scalingmentioning

confidence: 99%

“…So at one stage finding a Lax description for the dispersionless limit became an enigma. Anyway, it was resolved by Barcelos-Neto et al [2] in two ways: (A) Unlike the bosonic variables, fermionic variables need to scale for a consistent "classical" limit. Hence it can be checked that the"classical" limit involves the scaling ∂ → ǫ∂ and φ → ǫ −1/2 φ without which the fermion terms would not be present …”

Section: Construction Of Dispersionless Kuper-kdv Equation Via Scalingmentioning

confidence: 99%

Supersymmetric Kuper Camassa–holm Equation and Geodesic Flow: A Novel Approach

Guha

2008

Int. J. Geom. Methods Mod. Phys.

View full text Add to dashboard Cite

We use the logarithmic 2-cocycle and the action of V ect(S 1 ) on the space of Pseudo-differential symbols to derive one particular type of supersymmetric KdV equation, known as Kuper-KdV equation. This equation was formulated by Kupershmidt and it is different from the Manin-Radul-Mathieu type equation. The two Super KdV equations behave differently under a supersymmetric transformation and Kupershmidt version does not preserve SUSY transformation. In this paper we study the second type of supersymmetric generalization of the Camassa-Holm equation correspoding to Kuper-KdV equation via standard embedding of super vector fields into the Lie algebra of graded peudodifferential symbols. The natural lift of the action of superconformal group SDif f yields SDif f module. This method is particularly useful to construct Moyal quantized systems.Mathematical Classification 17B68, 37K10, 58J40.1

show abstract

“…The first term on the right hand side represents the nonlinear term. Let us, for a moment, look at the KdV equation without the nonlinear term, namely, ∂u ∂t = ∂ 3 u ∂x 3 (6) It is easy to write down the dispersion relation following from this equation,…”

Section: Non-dispersive Solutionsmentioning

confidence: 99%