A new integrable symplectic map by the binary nonlinearization to the super AKNS system

被引：66

作者：

Li, Xin-Yue ^{[1
,2
]}

Zhao, Qiu-Lan ^{[1
]}

机构：

[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

[2] Key Lab Robot & Intelligent Technol Shandong Prov, Qingdao 266590, Peoples R China

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2017年 / 121卷

关键词：

Orthosymplectic Lie superalgebras; Super AKNS hierarchy; Explicit symmetry constraint; Binary nonlinearization; HAMILTONIAN-STRUCTURE; SYMMETRY CONSTRAINTS; MKDV HIERARCHY; LIE-ALGEBRAS; EQUATION; REPRESENTATIONS;

D O I：

10.1016/j.geomphys.2017.07.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Based on the constructed new Lie super-algebra from OSP(2,2), the super bi-Hamiltonian structure of a new super AKNS hierarchy is obtained by making use of super-trace identity. For the new super AKNS system, an explicit symmetry constraint between the potentials and the eigenfunctions is proposed. Moreover, the super AKNS system is decomposed into two compatible finite-dimensional super integrable systems and the obtained super systems are proved to be finite-dimensional super integrable Hamiltonian systems in the super-symmetry manifold R-4N/4N. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：123 / 137

页数：15

共 59 条

[1] UNITARY REPRESENTATIONS OF NON-COMPACT SUPERGROUPS [J].

BARS, I ;

GUNAYDIN, M .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1983, 91 (01) :31-51

[2]

Belokolos E. D., 1994, Algebro-geometric approach to nonlinear integrable equations

[3]

CAO CW, 1990, SCI CHINA SER A, V33, P528

[4] THE CONSTRAINT OF THE KADOMTSEV-PETVIASHVILI EQUATION AND ITS SPECIAL SOLUTIONS [J].

CHENG, Y ;

LI, YS .

PHYSICS LETTERS A, 1991, 157 (01) :22-26

[5] ALL POSSIBLE SYMMETRIES OF S MATRIX [J].

COLEMAN, S ;

MANDULA, J .

PHYSICAL REVIEW, 1967, 159 (05) :1251-&

[6] GRADED LIE-ALGEBRAS IN MATHEMATICS AND PHYSICS (BOSE-FERMI SYMMETRY) [J].

CORWIN, L ;

NEEMAN, Y ;

STERNBERG, S .

REVIEWS OF MODERN PHYSICS, 1975, 47 (03) :573-603

[7]

Curses M., 1985, PHYS LETT, V108, P437

[8] Realizations of the Lie superalgebra q(2) and applications [J].

Debergh, N ;

Van der Jeugt, J .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (39) :8119-8133

[9] Generalized fractional supertrace identity for Hamiltonian structure of NLS-MKdV hierarchy with self-consistent sources [J].

Dong, Huan He ;

Guo, Bao Yong ;

Yin, Bao Shu .

ANALYSIS AND MATHEMATICAL PHYSICS, 2016, 6 (02) :199-209

[10] The new integrable symplectic map and the symmetry of integrable nonlinear lattice equation [J].

Dong, Huanhe ;

Zhang, Yong ;

Zhang, Xiaoen .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2016, 36 :354-365

← 1 2 3 4 5 6 →