Binary Nonlinearization of the Super Akns System

He, Jingsong; Yu, Jing; Cheng, Yi; Zhou, Ruguang

doi:10.1142/s0217984908014778

Cited by 49 publications

(70 citation statements)

References 27 publications

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“…In very recent years, nonlinearization of the super AKNS system has been studied in Ref. [20], where we considered an explicit symmetry constraint of the super AKNS system, and we proved that under the explicit constraint, the super AKNS system was completely integrable super Hamiltonian system in the Liouville sense. Inspired by this and implicit constraint of the classical integrable system, a natural question is appeared whether an implicit symmetry constraint is available for the super AKNS system.…”

Section: Introductionmentioning

confidence: 77%

Binary nonlinearization of the super AKNS system under an implicit symmetry constraint

Han

2009

J. Phys. A: Math. Theor.

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For the super AKNS system, an implicit symmetry constraint between the potentials and the eigenfunctions is proposed. After introducing some new variables to explicitly express potentials, the super AKNS system is decomposed into two compatible finite-dimensional super systems (x-part and t n -part). Furthermore, we show that the obtained super systems are integrable super Hamiltonian systems in supersymmetry manifold R 4N +2|2N +2 .

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Section: Introductionmentioning

confidence: 77%

Binary nonlinearization of the super AKNS system under an implicit symmetry constraint

Han

2009

J. Phys. A: Math. Theor.

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“…In addition, similar to [16], we know that and { } =1 , we can use the method in [16], or the technique by ma etal [23,24]. Therefore, the 3 functions { } =1 2 and { } =1 , are functional independent over some region of the super symmetry manifold ℝ 4 |2 .…”

Section: Binary Nonlinearization Of Super Guo Hierarchymentioning

confidence: 99%

“…Studies provide many examples of super symmetry integrable systems, with super dependent variables and/or super independent variables [11]- [15]. Only very recently, nonlinearization were made for the super AKNS hierarchy , the super Dirac hierarchy and their corresponding super finite dimensional hierarchies were generated [16]- [18]. Li and Dong presented the super Hamiltonian structures of the super Guo hierarchy [19].…”

Section: Introductionmentioning

confidence: 99%

Bargmann Symmetry Constraint and Binary Nonlinearization of Super Guo Hierarchy

Tao¹

2013

IJAPM

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Abstract-An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Guo hierarchy. Under the obtained symmetry constraint, the n-th flow of the super Guo hierarchy is decomposed into two super finite -dimensional integrable Hamiltonian systems, which defined over the super symmetry manifold R 4N|2N with the corresponding dynamical variables x and t n . The integrals of motion required for Liouville integrability are explicitly given.Index Terms-Symmetry constraint, binary nonlinearization, super guo hierarchy, super finitee-dimensional integrable hamiltonian systems. I. INTRODUCTIONFor almost twenty years, much attention has been paid to the construction of finite-dimensional integrable systems from soliton equations by using symmetry constraints. Either [19]. In this paper, we would like to consider the binary nonlinearization of the super Guo hierarchy. This paper is organized as follows. In the next section, we will recall the super Guo soliton hierarchy and its super Hamiltonian structure. Then in Section III, we compute a Bargmann symmetry constraint for the potential of the super Guo hierarchy. In Section IV, we apply the binary nonlinearization method to super Guo hierarchy, and then obtain super finite-dimensional integrable Hamiltonian hierarchy on the super symmetry manifold ℝ 4 |2 , whose integrals of motion are explicitly given. II. THE SUPER GUO HIERARCHYwhere is a spectral parameter, q and r are even variables, and and are odd variables(see [20] ). Taking If we setthen (2) Si-Xing TaoBargmann Symmetry Constraint and Binary Nonlinearization of Super Guo Hierarchy

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“…Several super integrable systems including super AKNS hierarchy, super KdV hierarchyand super classical Boussinseq hierarchy, etc., have been studied [1]- [4]. There are some interesting results on the super integrable systems, such as Darboux transformation [5], super Hamiltonian structures [6], binary nonlinearization [7] and reciprocal transformation [8] and so on.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Super Integrable Couplings of Super Classical Boussinesq Hierarchy

Tao¹,

Shi²

2015

IJAPM

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Enlargement of Lie super algebra B(0, 1) was given firstly. Then nonlinear super integrable couplings of the super classical Boussinesq hierarchy based upon this enlarged matrix Lie super algebra were constructed secondly. And its super Hamiltonian structures were established by using super trace identity thirdly. As its reduction, special integrable couplings of classical Boussinesq hierarchy were obtained finally.

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Binary Nonlinearization of the Super Akns System

Cited by 49 publications

References 27 publications

Binary nonlinearization of the super AKNS system under an implicit symmetry constraint

Binary nonlinearization of the super AKNS system under an implicit symmetry constraint

Bargmann Symmetry Constraint and Binary Nonlinearization of Super Guo Hierarchy

Nonlinear Super Integrable Couplings of Super Classical Boussinesq Hierarchy

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