TY - JOUR

T1 - An approach for constructing loop algebra via exterior algebra and its applications

AU - TAM, Hon Wah

AU - Zhang, Yu Feng

N1 - Funding Information:
This research is supported by Hong Kong Research Grant Council grant RGC/2016/03p. The authors are grateful to Professor M. Wadati for his enthusiastic guidance and help.

PY - 2005/1

Y1 - 2005/1

N2 - With the help of some properties of exterior algebra defined by us, a general approach for constructing multi-component matrix loop algebra is proposed. By making use of the approach, a new 3M loop algebra X is constructed. This algebra can be easily reduced to the existing multi-component loop algebra. Another an new extended loop algebra Y is also presented. As their applicable examples, a generalized multi-component AKNS hierarchy with arbitrary smooth functions and a generalized multi-component KN hierarchy are worked out. As a reduction cases of the first hierarchy, the standard multi-component heat-conduction equation and a coupled generalized multi-component Burgers equation are given. The approach presented in the paper can be used generally.

AB - With the help of some properties of exterior algebra defined by us, a general approach for constructing multi-component matrix loop algebra is proposed. By making use of the approach, a new 3M loop algebra X is constructed. This algebra can be easily reduced to the existing multi-component loop algebra. Another an new extended loop algebra Y is also presented. As their applicable examples, a generalized multi-component AKNS hierarchy with arbitrary smooth functions and a generalized multi-component KN hierarchy are worked out. As a reduction cases of the first hierarchy, the standard multi-component heat-conduction equation and a coupled generalized multi-component Burgers equation are given. The approach presented in the paper can be used generally.

UR - http://www.scopus.com/inward/record.url?scp=4243053690&partnerID=8YFLogxK

U2 - 10.1016/j.chaos.2004.05.007

DO - 10.1016/j.chaos.2004.05.007

M3 - Article

AN - SCOPUS:4243053690

VL - 23

SP - 535

EP - 541

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

IS - 2

ER -