TY - JOUR
T1 - Invertible linear transformations and the Lie algebras
AU - Zhang, Yufeng
AU - Tam, Honwah
AU - Guo, Fukui
N1 - Funding Information:
This work was supported by The National Science Foundation of China (10471139) and Hong Kong Research Grant Council grant number HKBU RGC 2016/05p.
PY - 2008/7
Y1 - 2008/7
N2 - With the help of invertible linear transformations and the known Lie algebras, a way to generate new Lie algebras is given. These Lie algebras obtained have a common feature, i.e. integrable couplings of solitary hierarchies could be obtained by using them, specially, the Hamiltonian structures of them could be worked out. Some ways to construct the loop algebras of the Lie algebras are presented. It follows that some various loop algebras are given. In addition, a few new Lie algebras are explicitly constructed in terms of the classification of Lie algebras proposed by Ma Wen-Xiu, which are bases for obtaining new Lie algebras by using invertible linear transformations. Finally, some solutions of a (2 + 1)-dimensional partial-differential equation hierarchy are obtained, whose Hamiltonian form-expressions are manifested by using the quadratic-form identity.
AB - With the help of invertible linear transformations and the known Lie algebras, a way to generate new Lie algebras is given. These Lie algebras obtained have a common feature, i.e. integrable couplings of solitary hierarchies could be obtained by using them, specially, the Hamiltonian structures of them could be worked out. Some ways to construct the loop algebras of the Lie algebras are presented. It follows that some various loop algebras are given. In addition, a few new Lie algebras are explicitly constructed in terms of the classification of Lie algebras proposed by Ma Wen-Xiu, which are bases for obtaining new Lie algebras by using invertible linear transformations. Finally, some solutions of a (2 + 1)-dimensional partial-differential equation hierarchy are obtained, whose Hamiltonian form-expressions are manifested by using the quadratic-form identity.
KW - Invertible linear transformation
KW - Lie algebra
KW - Soliton hierarchy
UR - http://www.scopus.com/inward/record.url?scp=35449007969&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2006.07.011
DO - 10.1016/j.cnsns.2006.07.011
M3 - Journal article
AN - SCOPUS:35449007969
SN - 1007-5704
VL - 13
SP - 682
EP - 702
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
IS - 4
ER -