HOW TO CONSTRUCT FINITE-DIMENSIONAL BI-HAMILTONIAN SYSTEMS FROM SOLITON-EQUATIONS - JACOBI INTEGRABLE POTENTIALS

被引：48

作者：

ANTONOWICZ, M ^{[1
]}

RAUCHWOJCIECHOWSKI, S ^{[1
]}

机构：

[1] LINKOPING UNIV,DEPT MATH,S-58183 LINKOPING,SWEDEN

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 1992年 / 33卷 / 06期

关键词：

D O I：

10.1063/1.529632

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A systematic method of constructing finite-dimensional integrable systems starting from a bi-Hamiltonian hierarchy of soliton equations is introduced. The existence of two Hamiltonian structures of the hierarchy leads to a bi-Hamiltonian formulation of the resulting finite-dimensional systems. The case of coupled KdV hierarchies is studied in detail. A surprising connection with separable Jacobi potentials is uncovered and described.

引用

页码：2115 / 2125

页数：11

共 45 条

[1] Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints
Manukure, Solomon
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2018, 57 : 125 - 135
[2] A hierarchy of nonlinear evolution equations, its bi-Hamiltonian structure, and finite-dimensional integrable systems
Fan, EG
Zhang, HQ
JOURNAL OF MATHEMATICAL PHYSICS, 2000, 41 (04) : 2058 - 2065
[3] GAUGE TRANSFORMATION AND BI-HAMILTONIAN STRUCTURE OF A FINITE-DIMENSIONAL INTEGRABLE SYSTEM REDUCED FROM A SOLITON EQUATION
ZENG, YB
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1991, 24 (01): : L11 - L16
[4] A Lax integrable hierarchy, bi-Hamiltonian structure and finite-dimensional Liouville integrable involutive systems
Xia, TC
Chen, XH
Chen, DY
CHAOS SOLITONS & FRACTALS, 2004, 22 (04) : 939 - 945
[5] A GENERALIZED KAUP-NEWELL SPECTRAL PROBLEM, SOLITON-EQUATIONS AND FINITE-DIMENSIONAL INTEGRABLE SYSTEMS
GENG, XG
MA, WX
NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA A-NUCLEI PARTICLES AND FIELDS, 1995, 108 (04): : 477 - 486
[6] BI-HAMILTONIAN FORMULATION OF A FINITE-DIMENSIONAL INTEGRABLE SYSTEM REDUCED FROM A LAX HIERARCHY OF THE KDV
BLASZAK, M
BASARABHORWATH, P
PHYSICS LETTERS A, 1992, 171 (1-2) : 45 - 51
[7] Integrable evolution systems based on Gerdjikov-Ivanov equations, bi-Hamiltonian structure, finite-dimensional integrable systems and N-fold Darboux transformation
Fan, EG
JOURNAL OF MATHEMATICAL PHYSICS, 2000, 41 (11) : 7769 - 7782
[8] A hierarchy of the Lax integrable system, its bi-Hamiltonian structure, finite-dimensional integrable system and involutive solution
Yan, ZY
CHAOS SOLITONS & FRACTALS, 2002, 13 (04) : 741 - 748
[9] Integrable Bi-Hamiltonian Systems by Jacobi Structure on Real Three-Dimensional Lie Groups
Amirzadeh-Fard, H.
Haghighatdoost, Gh.
Rezaei-Aghdam, A.
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2023, 30 (04) : 1483 - 1509
[10] Integrable bi-Hamiltonian systems by Jacobi structure on real three-dimensional Lie groups
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz
53714-161, Iran
不详
53714-161, Iran
不详
arXiv, 1600,

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