A hierarchy of the Lax integrable system, its bi-Hamiltonian structure, finite-dimensional integrable system and involutive solution

2002 ◽  
Vol 13 (4) ◽  
pp. 741-748 ◽  
Author(s):  
Zhenya Yan
Keyword(s):  
Integrable System ◽  
Hamiltonian Structure ◽  
Finite Dimensional

The Binary Nonlinearization of the Super Integrable System and Its Self-Consistent Sources

2017 ◽  
Vol 18 (3-4) ◽  
pp. 285-292 ◽  
Author(s):  
Beibei Hu ◽  
Tiecheng Xia
Keyword(s):  
Conservation Laws ◽  
Integrable System ◽  
Hamiltonian Structure ◽  
Trace Identity ◽  
Liouville Integrability ◽  
Integrals Of Motion ◽  
Symmetry Constraint ◽  
Finite Dimensional ◽  
Self Consistent ◽  
Super Lie Algebra

AbstractThe super integrable system and its super Hamiltonian structure are established based on a loop super Lie algebra and super-trace identity in this paper. Then the super integrable system with self-consistent sources and conservation laws of the super integrable system are constructed. Furthermore, an explicit Bargmann symmetry constraint and the binary nonlinearization of Lax pairs for the super integrable system are established. Under the symmetry constraint,the $n$-th flow of the super integrable system is decomposed into two super finite-dimensional integrable Hamilton systems over the supersymmetric manifold. The integrals of motion required for Liouville integrability are explicitly given.

The finite-dimensional super integrable system of a super NLS-mKdV equation

2012 ◽  
Vol 17 (11) ◽  
pp. 4044-4052 ◽  
Author(s):  
Qiu-Lan Zhao ◽  
Yu-Xia Li ◽  
Xin-Yue Li ◽  
Ye-Peng Sun
Keyword(s):  
Integrable System ◽  
Mkdv Equation ◽  
Finite Dimensional

The Bargmann Constraint and Integrable System for a Second-Order Spectral Problem

2015 ◽  
Vol 70 (11) ◽  
pp. 913-917
Author(s):  
Wei Liu ◽  
Yafeng Liu ◽  
Shujuan Yuan
Keyword(s):  
Coordinate System ◽  
Spectral Problem ◽  
Integrable System ◽  
Evolution Equations ◽  
Lagrange Equations ◽  
Lax Pairs ◽  
Infinite Dimensional ◽  
Hamilton System ◽  
Finite Dimensional ◽  
Dimensional Soliton

AbstractIn this article, the Bargmann system related to the spectral problem (∂2+q∂+∂q+r)φ=λφ+λφx is discussed. By the Euler–Lagrange equations and the Legendre transformations, a suitable Jacobi–Ostrogradsky coordinate system is obtained. So the Lax pairs of the aforementioned spectral problem are nonlinearised. A new kind of finite-dimensional Hamilton system is generated. Moreover, the involutive solutions of the evolution equations for the infinite-dimensional soliton system are derived.

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