Hamiltonian Tri-Integrable Couplings of the AKNS Hierarchy

2013 ◽  
Vol 59 (4) ◽  
pp. 385-392 ◽  
Author(s):  
Meng Jing-Han ◽  
Ma Wen-Xiu
Keyword(s):  
Akns Hierarchy ◽  
Integrable Couplings

HAMILTONIAN STRUCTURES OF TWO INTEGRABLE COUPLINGS OF THE MODIFIED AKNS HIERARCHY

2007 ◽  
Vol 21 (30) ◽  
pp. 2063-2074 ◽  
Author(s):  
YUFENG ZHANG ◽  
Y. C. HON
Keyword(s):  
Lie Algebra ◽  
Hamiltonian Structure ◽  
Three Dimensional ◽  
Hamiltonian Structures ◽  
Akns Hierarchy ◽  
Higher Dimensional ◽  
Integrable Couplings

The extension of a three-dimensional Lie algebra into two higher-dimensional ones is used to deduce two new integrable couplings of the m-AKNS hierarchy. The Hamiltonian structures of the two integrable couplings are obtained, respectively. Specially, the complex Hamiltonian structure of the second integrable couplings is given.

Integrable couplings of a generalized AKNS hierarchy

2002 ◽  
Vol 9 (3) ◽  
pp. 220-223 ◽  
Author(s):  
Yu-feng Zhang ◽  
Hong-qing Zhang ◽  
Qing-you Yan
Keyword(s):  
Akns Hierarchy ◽  
Integrable Couplings

SPECTRAL RADIUS ANALYSIS OF MATRICES AND THE ASSOCIATED WITH INTEGRABLE SYSTEMS

2009 ◽  
Vol 23 (24) ◽  
pp. 4855-4879 ◽  
Author(s):  
HONWAH TAM ◽  
YUFENG ZHANG
Keyword(s):  
Lie Algebra ◽  
Spectral Radius ◽  
Integrable Systems ◽  
Hamiltonian Structure ◽  
Soliton Equation ◽  
Spectral Matrix ◽  
Akns Hierarchy ◽  
Integrable Couplings ◽  
Isospectral Problem ◽  
Set Up

An isospectral problem is introduced, a spectral radius of the corresponding spectral matrix is obtained, which enlightens us to set up an isospectral problem whose compatibility condition gives rise to a zero curvature equation in formalism, from which a Lax integrable soliton equation hierarchy with constraints of potential functions is generated along with 5 parameters, whose reduced cases present three integrable systems, i.e., AKNS hierarchy, Levi hierarchy and D-AKNS hierarchy. Enlarging the above Lie algebra into two bigger ones, the two integrable couplings of the hierarchy are derived, one of them has Hamiltonian structure by employing the quadratic-form identity or variational identity. The corresponding integrable couplings of the reduced systems are obtained, respectively. Finally, as comparing study for generating expanding integrable systems, a Lie algebra of antisymmetric matrices and its corresponding loop algebra are constructed, from which a great number of enlarging integrable systems could be generated, especially their Hamiltonian structure could be computed by the trace identity.

scholarly journals A Few Integrable Couplings of Some Integrable Systems and (2+1)-Dimensional Integrable Hierarchies

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Binlu Feng ◽  
Yufeng Zhang ◽  
Huanhe Dong
Keyword(s):  
Lie Algebras ◽  
Integrable Systems ◽  
Integrable Hierarchies ◽  
Coupling Model ◽  
High Dimensional ◽  
Akns Hierarchy ◽  
Integrable Couplings ◽  
Integrable Coupling

Two high-dimensional Lie algebras are presented for which four (1+1)-dimensional expanding integrable couplings of the D-AKNS hierarchy are obtained by using the Tu scheme; one of them is a united integrable coupling model of the D-AKNS hierarchy and the AKNS hierarchy. Then (2+1)-dimensional DS hierarchy is derived by using the TAH scheme; in particular, the integrable couplings of the DS hierarchy are obtained.

scholarly journals A new approach for finding standard heat equation and a special Newell-whitehead equation

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1629-1636
Author(s):  
Xiu-Rong Guo ◽  
Yu-Feng Zhang ◽  
Mei Guo ◽  
Zheng-Tao Liu
Keyword(s):  
Heat Equation ◽  
Lie Algebras ◽  
Integrable Model ◽  
Block Matrix ◽  
Integrable Hierarchy ◽  
New Approach ◽  
Akns Hierarchy ◽  
Standard Heat ◽  
Integrable Couplings ◽  
Isospectral Problem

Under a frame of 2 ? 2 matrix Lie algebras, Tu and Meng [9] once established a united integrable model of the Ablowitz-Kaup-Newel-Segur (AKNS) hierarchy, the D-AKNS hierarchy, the Levi hierarchy and the TD hierarchy. Based on this idea, we introduce two block-matrix Lie algebras to present an isospectral problem, whose compatibility condition gives rise to a type of integrable hierarchy which can be reduced to the Levi hierarchy and the AKNS hierarchy, and so on. A united integrable model obtained by us in the paper is different from that given by Tu and Meng. Specially, the main result in the paper can be reduced to two new various integrable couplings of the Levi hierarchy, from which we again obtain the standard heat equation and a special Newell-Whitehead equation.

A KIND OF NEW CONTINUOUS LIMITS OF AN INTEGRABLE COUPLING SYSTEM FOR DISCRETE AKNS HIERARCHY

2011 ◽  
Vol 25 (26) ◽  
pp. 3443-3454
Author(s):  
FA-JUN YU
Keyword(s):  
Spectral Problem ◽  
Lie Algebra ◽  
Continuous Limit ◽  
Soliton Equation ◽  
Akns Hierarchy ◽  
Complex Lattice ◽  
Coupling System ◽  
Integrable Couplings ◽  
Integrable Coupling

We present a kind of new continuous limits of an integrable coupling system for discrete AKNS hierarchy by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, a coupling lattice hierarchy is derived. It is shown that a new sequence of combinations of complex lattice spectral problem converges to the integrable couplings of soliton equation hierarchy, which has the integrable coupling system of AKNS hierarchy as a continuous limit.

Some 2+1 Dimensional Super-Integrable Systems

2015 ◽  
Vol 70 (10) ◽  
pp. 791-796 ◽  
Author(s):  
Yufeng Zhang ◽  
Honwah Tam ◽  
Jianqin Mei
Keyword(s):  
Diffusion Equation ◽  
Integrable Systems ◽  
Schrodinger Equation ◽  
Hamiltonian Structure ◽  
Nonlinear Schrodinger Equation ◽  
The Other ◽  
Trace Identity ◽  
Akns Hierarchy ◽  
Dimensional Diffusion ◽  
Integrable Couplings

AbstractIn the article, we make use of the binormial-residue-representation (BRR) to generate super 2+1 dimensional integrable systems. Using these systems, we can deduce a super 2+1 dimensional AKNS hierarchy, which can be reduced to a super 2+1 dimensional nonlinear Schrödinger equation. In particular, two main results are obtained. One of them is a set of super 2+1 dimensional integrable couplings. The other one is a 2+1 dimensional diffusion equation. The Hamiltonian structure of the super 2+1 dimensional hierarchy is derived by using the super-trace identity.

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