Painlevé Analysis for Supersymmetric Extensions of the Sawada-Kotera Equation

Li, Li; Zhang, Mengxia; Lv, Shuqiang

doi:10.1515/zna-2011-3-405

Cited by 2 publications

(3 citation statements)

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“…Therefore, we may say that the (semi-)discrete system ( 28) is a discrete version of the potential SSK system. Of course, we may follow [18] and study other continuum limits such as skew continuum limit or full continuum limit for the system (28), but such calculations will not be given here since they are somewhat cumbersome.…”

Section: Continuum Limitsmentioning

confidence: 99%

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Supersymmetric Sawada-Kotera Equation: Bäcklund-Darboux Transformations and Applications

Mao¹,

Liu²,

Xue³

2021

JNMP

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In this paper, we construct a Darboux transformation and the related Bäcklund transformation for the supersymmetric Sawada-Kotera (SSK) equation.The associated nonlinear superposition formula is also worked out. We demonstrate that these are natural extensions of the similar results of the Sawada-Kotera equation and may be applied to produce the solutions of the SSK equation. Also, we present two semi-discrete systems and show that the continuum limit of one of them goes to the SKK equation.

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Section: Continuum Limitsmentioning

confidence: 99%

“…It is interesting to note the SSK equation possesses odd Hamiltonian structures and is a bi-Hamiltonian system [36]. Subsequent works show that the SSK equation is associated with supersymmetric Kawamoto equation [29] and passes the Painlevé test [28].…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric Sawada-Kotera Equation: Bäcklund-Darboux Transformations and Applications

Mao¹,

Liu²,

Xue³

2021

JNMP

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“…Let us now construct the supersymmetric extension of the N = 5 equation by considering the same fermionic superfield Ψ(x, θ) = √ i ψ(x) + θu(x). To do that, we use the following direct extension procedure [45,52],…”

Section: Superextension For the N = 5 Equationmentioning

confidence: 99%

Defects in the supersymmetric mKdV hierarchy via Bäcklund transformations

Aguirre¹,

Retore²,

Gomes³

et al. 2018

J. High Energ. Phys.

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The integrability of the N = 1 supersymmetric modified Korteweg de-Vries (smKdV) hierarchy in the presence of defects is investigated through the construction of its super Bäcklund transformation. The construction of such transformation is performed by using essentially two methods: the Bäcklund-defect matrix approach and the superfield approach. Firstly, we employ the defect matrix associated to the hierarchy which turns out to be the same for the supersymmetric sinh-Gordon (sshG) model. The method is general for all flows and as an example we derive explicitly the Bäcklund equations in components for the first few flows of the hierarchy, namely t 3 and t 5 . Secondly, the supersymmetric extension of the Bäcklund transformation in the superspace formalism is constructed for those flows. Finally, this super Bäcklund transformation is employed to introduce type I defects for the supersymmetric mKdV hierarchy. Further integrability aspects by considering modified conserved quantities are derived from the defect matrix.

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Painlevé Analysis for Supersymmetric Extensions of the Sawada-Kotera Equation

Cited by 2 publications

References 0 publications

Supersymmetric Sawada-Kotera Equation: Bäcklund-Darboux Transformations and Applications

Supersymmetric Sawada-Kotera Equation: Bäcklund-Darboux Transformations and Applications

Defects in the supersymmetric mKdV hierarchy via Bäcklund transformations

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