On the integrability of three two-component bi-Hamiltonian systems

被引：0

作者：

Zang, Liming ^{[1
]}

Zhang, Qian ^{[2
]}

Liu, Q. P. ^{[2
]}

机构：

[1] Beijing Informat Sci & Technol Univ BISTU, Sch Appl Sci, Beijing 100192, Peoples R China

[2] China Univ Min & Technol, Dept Math, Beijing 100083, Peoples R China

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2024年 / 57卷 / 33期

基金：

中国国家自然科学基金;

关键词：

bi-Hamiltonian systems; prolongation structure; Lax representation; energy-dependent Schr & ouml; dinger operator; PROLONGATION STRUCTURES; CONSERVATION-LAWS; DEFORMATIONS; CLASSIFICATION; EQUATIONS;

D O I：

10.1088/1751-8121/ad65a1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The compatible trios of two-component homogeneous Hamiltonian operators were classified and some bi-Hamiltonian systems were constructed by Lorenzoni et al (2018 J. Phys. A: Math. Theor. 51 045202). In this paper, we study three two-component bi-Hamiltonian systems proposed by them. By means of the prolongation structure technique, we construct the missing Lax representations for those systems and confirm their integrability. Furthermore, we explore the possible connections between those systems and the known integrable systems.

引用

页数：18

共 50 条

[21] New bi-Hamiltonian systems on the plane
Tsiganov, A. V.
JOURNAL OF MATHEMATICAL PHYSICS, 2017, 58 (06)
[22] Bi-Hamiltonian partially integrable systems
Giachetta, G
Mangiarotti, L
Sardanashvily, G
JOURNAL OF MATHEMATICAL PHYSICS, 2003, 44 (05) : 1984 - 1997
[23] Bi-Hamiltonian systems of natural form
A. V. Tsyganov
Theoretical and Mathematical Physics, 2006, 149 : 1437 - 1456
[24] Bi-Hamiltonian systems of deformation type
Boualem, H.
Brouzet, R.
JOURNAL OF GEOMETRY AND PHYSICS, 2006, 56 (08) : 1370 - 1386
[25] Three-Component Generalisation of Burgers Equation and Its Bi-Hamiltonian Structures
Liu, Wei
Geng, Xianguo
Xue, Bo
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2017, 72 (05): : 469 - 475
[26] Bi-Hamiltonian systems of natural form
Tsyganov, A. V.
THEORETICAL AND MATHEMATICAL PHYSICS, 2006, 149 (02) : 1437 - 1456
[27] Separation of Variables for Bi-Hamiltonian Systems
Gregorio Falqui
Marco Pedroni
Mathematical Physics, Analysis and Geometry, 2003, 6 : 139 - 179
[28] INEQUIVALENT QUANTIZATIONS OF BI-HAMILTONIAN SYSTEMS
SCHERER, W
ZAKRZEWSKI, S
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1993, 26 (03): : L113 - L117
[29] Composite integrators for bi-Hamiltonian systems
Karasozen, B
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1996, 32 (07) : 79 - 86
[30] Separation of variables for bi-Hamiltonian systems
Falqui, G
Pedroni, M
MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 2003, 6 (02) : 139 - 179

← 1 2 3 4 5 →