A multi-component matrix loop algebra and the multi-component Kaup–Newell (KN) hierarchy, as well as its integrable coupling system

2007 ◽  
Vol 31 (2) ◽  
pp. 473-479 ◽  
Author(s):  
Wei Yuan ◽  
Yufeng Zhang ◽  
Yue Chao
Keyword(s):  
Loop Algebra ◽  
Coupling System ◽  
Integrable Coupling ◽  
Matrix Loop Algebra ◽  
Component Matrix

The Multi-Component Jaulent-Miodek Hierarchy and its Multi-Component Integrable Coupling System with Two Arbitrary Functions

2012 ◽  
Vol 442 ◽  
pp. 124-128
Author(s):  
Jian Ya Ge ◽  
Tie Cheng Xia
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Loop Algebra ◽  
Simple Loop ◽  
Coupling System ◽  
Integrable Couplings ◽  
Isospectral Problem ◽  
Integrable Coupling

We devise a new simple loop algebra GM and an isospectral problem. By making use of Tu scheme, the multi-component Jaulent-Miodek (JM) hierarchy is obtained. Furthermore, an expanding loop algebra FM of the loop algebra GM is presented. Based on FM the multi-component integrable couplings system with two arbitrary functions of the multi-component Jaulent-Miodek (JM) hierarchy are worked out. The method can be applied to other nonlinear evolution equations hierarchies.

(2+1)-DIMENSIONAL TD HIERARCHY AND ITS INTEGRABLE COUPLINGS

2007 ◽  
Vol 21 (07) ◽  
pp. 407-413 ◽  
Author(s):  
ZHU LI ◽  
HUAN-HE DONG
Keyword(s):  
Loop Algebra ◽  
Curvature Equation ◽  
Zero Curvature ◽  
Coupling System ◽  
Integrable Couplings ◽  
Integrable Coupling

Under the frame of the (2 + 1)-dimensional zero curvature equation and Tu model, the (2 + 1)-dimensional TD hierarchy is obtained. Again, by using the expanding loop algebra, the integrable coupling system of the above hierarchy is given.

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