A few new higher-dimensional Lie algebras and two types of coupling integrable couplings of the AKNS hierarchy and the KN hierarchy

2011 ◽  
Vol 16 (1) ◽  
pp. 76-85 ◽  
Author(s):  
Yu-Feng Zhang ◽  
Honwah Tam
Keyword(s):  
Lie Algebras ◽  
Akns Hierarchy ◽  
Higher Dimensional ◽  
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.

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.

Expansion of the Lie algebras and integrable couplings

2008 ◽  
Vol 38 (2) ◽  
pp. 541-547
Author(s):  
Wang Yan ◽  
Yufeng Zhang
Keyword(s):  
Lie Algebras ◽  
Integrable Couplings

A SOLITON HIERARCHY FROM THE LEVI SPECTRAL PROBLEM AND ITS TWO INTEGRABLE COUPLINGS, HAMILTONIAN STRUCTURE

2009 ◽  
Vol 23 (05) ◽  
pp. 731-739
Author(s):  
YONGQING ZHANG ◽  
YAN LI
Keyword(s):  
Spectral Problem ◽  
Lie Algebras ◽  
Hamiltonian Structure ◽  
Soliton Equation ◽  
Curvature Equation ◽  
Loop Algebras ◽  
Zero Curvature ◽  
Soliton Hierarchy ◽  
Integrable Couplings ◽  
Time Part

A soliton-equation hierarchy from the D. Levi spectral problem is obtained under the framework of zero curvature equation. By employing two various multi-component Lie algebras and the loop algebras, we enlarge the Levi spectral problem and the corresponding time-part isospectral problems so that two different integrable couplings are produced. Using the quadratic-form identity yields the Hamiltonian structure of one of the two integrable couplings.

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