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Indexed by:期刊论文
Date of Publication:2012-06-01
Journal:COMMUNICATIONS IN THEORETICAL PHYSICS
Included Journals:SCIE、ISTIC、Scopus
Volume:57
Issue:6
Page Number:1012-1022
ISSN No.: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.