On Bäcklund transformation for supersymmetric two-boson equation

Xue, Lingling; Liu, Q. P.

doi:10.1016/j.physleta.2013.01.043

Cited by 3 publications

(7 citation statements)

References 22 publications

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“…Remark 1: Up to a simple change of variables, the BT in the Case II coincides with the one appeared in the framework of super-Bell polynomials (see [18] or [19]).…”

Section: Darboux-bäcklund Transformationmentioning

confidence: 78%

“…For a given a Bäcklund transformation, it is interesting to find the corresponding nonlinear superposition formula. For the Case II of the last section, such formula has been worked out already in [19]. In this section, we consider the nonlinear superposition formula for the Bäcklund transformation given in the Case I.…”

Section: Nonlinear Superposition Formulamentioning

confidence: 99%

“…Recently, by means of super-Bell polynomials, Fan obtained the bilinear Bäcklund transformation for it [18]. Very recently, Xue and one of the authors examined Fan's Bäcklund transformation and worked out its related nonlinear superposition formula [19].…”

Section: Introductionmentioning

confidence: 99%

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Darboux transformations for supersymmetric two-boson equation

Niu,

Liu,

Xue

2017

Preprint

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“…Remark 1: Up to a simple change of variables, the BT in the Case II coincides with the one appeared in the framework of super-Bell polynomials (see [18] or [19]).…”

Section: Darboux-bäcklund Transformationmentioning

confidence: 78%

Section: Nonlinear Superposition Formulamentioning

confidence: 99%

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Darboux transformations for supersymmetric two-boson equation

Niu,

Liu,

Xue

2017

Preprint

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“…[28] By using the bi-logarithmic transformations (7), one can convert the coupled system (26) into the bilinear MKdV system (2). Thus, this system (25) deserves the name of the supersymmetric MKdV (SMKdV) system.…”

Section: Symmetry Algebras Of the Snkp Systemmentioning

confidence: 99%

“…However, this seemingly simple extension is not trivial and worth further considerations, as the Hirota bilinear method is powerful and effective not only for finding soliton solutions but also for searching new integrable systems in the classic [16,[19][20][21] and supersymmetric [22] contexts. The coupled system (3) can also be viewed as a (2+1)-dimensional generalization of the bilinear supersymmetric two-boson system, [13,[23][24][25][26] since it reduces to the supersymmetric two-boson system when y = x.…”

Section: Introductionmentioning

confidence: 99%

Constructing (2+1)-dimensional ${\mathscr{N}}=1$ supersymmetric integrable systems from the Hirota formalism in the superspace

2018

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The 𝒩 = 1 supersymmetric extensions of two integrable systems, a special negative Kadomtsev-Petviashvili (NKP) system and a (2+1)-dimensional modified Korteweg-de Vries (MKdV) system, are constructed from the Hirota formalism in the superspace. The integrability of both systems in the sense of possessing infinitely many generalized symmetries are confirmed by extending the formal series symmetry approach to the supersymmetric framework. It is found that both systems admit a generalization of W ∞ type algebra and a Kac-Moody-Virasoro type subalgebra. Interestingly, the first one of the positive flow of the supersymmetric NKP system is another 𝒩 = 1 supersymmetric extension of the (2+1)-dimensional MKdV system. Based on our work, a hypothesis is put forward on a series of (2+1)-dimensional supersymmetric integrable systems. It is hoped that our work may develop a straightforward way to obtain supersymmetric integrable systems in high dimensions.

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