The fractional quadratic-form identity and Hamiltonian structure of an integrable coupling of the fractional Ablowitz-Kaup-Newell-Segur hierarchy

2013 ◽  
Vol 54 (7) ◽  
pp. 073518 ◽  
Author(s):  
Chao Yue ◽  
Tiecheng Xia
Keyword(s):  
Quadratic Form ◽  
Hamiltonian Structure ◽  
Integrable Coupling

scholarly journals A Hierarchy of Discrete Integrable Coupling System with Self-Consistent Sources

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yuqing Li ◽  
Huanhe Dong ◽  
Baoshu Yin
Keyword(s):  
Quadratic Form ◽  
Hamiltonian Structure ◽  
Liouville Integrability ◽  
Soliton Equation ◽  
Coupling System ◽  
Self Consistent ◽  
Integrable Coupling

Integrable coupling system of a lattice soliton equation hierarchy is deduced. The Hamiltonian structure of the integrable coupling is constructed by using the discrete quadratic-form identity. The Liouville integrability of the integrable coupling is demonstrated. Finally, the discrete integrable coupling system with self-consistent sources is deduced.

scholarly journals The Fractional Quadratic-Form Identity and Hamiltonian Structure of an Integrable Coupling of the Fractional Broer-Kaup Hierarchy

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Chao Yue ◽  
Tiecheng Xia ◽  
Guijuan Liu ◽  
Jianbo Liu
Keyword(s):  
Quadratic Form ◽  
Fractional Order ◽  
Hamiltonian Structure ◽  
Integrable Couplings ◽  
Isospectral Problem ◽  
Integrable Coupling

A fractional quadratic-form identity is derived from a general isospectral problem of fractional order, which is devoted to constructing the Hamiltonian structure of an integrable coupling of the fractional BK hierarchy. The method can be generalized to other fractional integrable couplings.

scholarly journals On (2+1)-dimensional expanding integrable model of the Davey-Stewartson hierarchy

2021 ◽  
Vol 25 (6 Part B) ◽  
pp. 4431-4439
Author(s):  
Xiu-Rong Guo ◽  
Fang-Fang Ma ◽  
Juan Wang
Keyword(s):  
Lie Algebras ◽  
Hamiltonian Structure ◽  
Integrable Model ◽  
Coupling System ◽  
Integrable Coupling ◽  
Type Abstraction Hierarchy

This paper mainly investigates the reductions of an integrable coupling of the Levi hierarchy and an expanding model of the (2+1)-dimensional Davey-Stewartson hierarchy. It is shown that the integrable coupling system of the Levi hierarchy possesses a quasi-Hamiltonian structure under certain constraints. Based on the Lie algebras construct, The type abstraction hierarchy scheme is used to gener?ate the (2+1)-dimensional expanding integrable model of the Davey-Stewartson hierarchy.

scholarly journals The Semidirect Sum of Lie Algebras and Its Applications to C-KdV Hierarchy

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xia Dong ◽  
Tiecheng Xia ◽  
Desheng Li
Keyword(s):  
Quadratic Form ◽  
Lie Algebras ◽  
Integrable Systems ◽  
The Other ◽  
Loop Algebra ◽  
Hamiltonian Structures ◽  
Kdv Hierarchy ◽  
Integrable Coupling

By use of the loop algebraG-~, integrable coupling of C-KdV hierarchy and its bi-Hamiltonian structures are obtained by Tu scheme and the quadratic-form identity. The method can be used to produce the integrable coupling and its Hamiltonian structures to the other integrable systems.

A solitary hierarchy of an integrable coupling and its Hamiltonian structure☆

2007 ◽  
Vol 34 (3) ◽  
pp. 914-918 ◽  
Author(s):  
Yu-Feng Zhang ◽  
Si-Hong Nian ◽  
En-Gui Fan
Keyword(s):  
Hamiltonian Structure ◽  
Integrable Coupling

THE INTEGRABLE PROPERTY OF LOTKA–VOLTERRA TYPE DISCRETE NONLINEAR LATTICE SOLITON SYSTEMS

2008 ◽  
Vol 22 (21) ◽  
pp. 2007-2019 ◽  
Author(s):  
XIN-YUE LI ◽  
XI-XIANG XU ◽  
QIU-LAN ZHAO
Keyword(s):  
Conservation Laws ◽  
Algebraic System ◽  
Hamiltonian Structure ◽  
Volterra Type ◽  
Soliton Equation ◽  
Nonlinear Lattice ◽  
Integrable Coupling

A hierarchy of discrete lattice soliton equation is obtained by using a novel algebraic system, and its Hamiltonian structure is generated by use of the Tu model. Then, conservation laws and integrable coupling of the obtained equation hierarchies are discussed.

INTEGRABLE HAMILTONIAN HIERARCHIES ASSOCIATED WITH THE EQUATION OF HEAT CONDUCTION

2010 ◽  
Vol 24 (14) ◽  
pp. 1573-1594 ◽  
Author(s):  
YUFENG ZHANG ◽  
HONWAH TAM ◽  
JIANQIN MEI
Keyword(s):  
Heat Conduction ◽  
Quadratic Form ◽  
Lie Algebra ◽  
Hamiltonian Structure ◽  
Evolution Equations ◽  
Arbitrary Parameter ◽  
Higher Dimensional ◽  
Soliton Hierarchy ◽  
Equation Of Heat Conduction ◽  
Hamiltonian Functions

Using a 4-dimensional Lie algebra g, an isospectral Lax pair is introduced, whose compatibility condition is equivalent to a soliton hierarchy of evolution equations with three components of potential functions. Its Hamiltonian structure is obtained by employing the quadratic-form identity proposed by Guo and Zhang. In order to obtain explicit Hamiltonian functions, a detailed computing formula for the constant appearing in the quadratic-form identity is obtained. One type of reduction equations of the hierarchy is also produced, which is further reduced to the standard equation of heat conduction. By introducing a loop algebra of the Lie algebra g, we obtain a soliton hierarchy with an arbitrary parameter which can be reduced to the previous equation hierarchy obtained, whose quasi-Hamiltonian structure is also worked out by the quadratic-form identity. Finally, we extend the Lie algebra g into a higher-dimensional Lie algebra so that a new integrable Hamiltonian hierarchy, which comprise integrable couplings, is produced; its reduced equations in particular contain two arbitrary parameters.

Sign in / Sign up

Export Citation Format

Share Document