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

Yu, Jing; Han, Jingwei; He, Jingsong

doi:10.1088/1751-8113/42/46/465201

Cited by 32 publications

(24 citation statements)

References 27 publications

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“…The discrete version of classical integrable systems, as an important field of soliton and integrable systems, has been discussed extensively by the binary nonlinearization method [9][10][11]. At the same time, the counterparts of binary nonlinearization associated with super-continuous integrable hierachy are deduced widely recently [12][13][14]. However, literatures we found were mainly concentrated in binary nonlinearization of discrete integrable systems associated with lower-order matrix spectral problems [15][16][17][18].…”

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A Bargmann system and the involutive solutions associated with a new 4-order lattice hierarchy

Zhao

2015

Anal.Math.Phys.

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By means of the nonlinearization technique, a Bargmann constraint associated with a new discrete 4 × 4 matrix eigenvalue problem is proposed, and a new symplectic map of the Bargmann type is obtained through binary nonlinearization of the discrete eigenvalue problem and its adjoint one. Moreover, the generating function of integrals of motion is obtained, by which the symplectic map is further proved to be completely integrable in the Liouville sense. Finally, the involutive representation of solutions are given.

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A Bargmann system and the involutive solutions associated with a new 4-order lattice hierarchy

Zhao

2015

Anal.Math.Phys.

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“…The following result is a general formula for the variational derivative with respect to the potential u (see [3] for the classical case). Lemma 1 [17]- [19] Let ( , ) be an even matrix of order + depending on , , , ⋯, and a parameter . Suppose that = , and = , satisfy the spectral problem and the adjoint spectral problem…”

Section: Bargmann Symmetry Constraint Of Super Guo Hierarchymentioning

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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“…In what follows, we will make an application to the super AKNS hierarchy [20][21][22][23][24][25] to shed light on this generating scheme.…”

Section: Constructing Nonlinear Super Integrable Couplingsmentioning

confidence: 99%

Nonlinear super integrable Hamiltonian couplings

You

2011

Journal of Mathematical Physics

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Based on a kind of new Lie superalgebras, we proposed a scheme for constructing nonlinear super integrable couplings. Super trace identity over the corresponding loop superalgebras is used to furnish the super Hamiltonian structures for the resulting nonlinear super integrable couplings. We illustrate the application of the scheme by means of an enlarged super Ablowitz-Kaup-Newell-Segur (AKNS) matrix spectral problem and present a nonlinear super integrable Hamiltonian couplings for the super AKNS hierarchy. C

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

Cited by 32 publications

References 27 publications

A Bargmann system and the involutive solutions associated with a new 4-order lattice hierarchy

A Bargmann system and the involutive solutions associated with a new 4-order lattice hierarchy

Bargmann Symmetry Constraint and Binary Nonlinearization of Super Guo Hierarchy

Nonlinear super integrable Hamiltonian couplings

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