Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2012-06-01

Journal: COMMUNICATIONS IN THEORETICAL PHYSICS

Included Journals: Scopus、ISTIC、SCIE

Volume: 57

Issue: 6

Page Number: 1012-1022

ISSN: 0253-6102

Key Words: Lie algebra; integrable system; elliptic variable solution

Abstract: A 3 x 3 matrix Lie algebra is first introduced, its subalgebras and the generated Lie algebras are obtained, respectively. Applications of a few Lie subalgebras give rise to two integrable nonlinear hierarchies of evolution equations from their reductions we obtain the nonlinear Schrodinger equations, the mKdV equations, the Broer-Kaup (BK) equation and its generalized equation, etc. The linear and nonlinear integrable couplings of one integrable hierarchy presented in the paper are worked out by casting a 3 x 3 Lie subalgebra into a 2 x 2 matrix Lie algebra. Finally, we discuss the elliptic variable solutions of a generalized BK equation.