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论文类型：期刊论文

发表时间：2012-06-01

发表刊物：COMMUNICATIONS IN THEORETICAL PHYSICS

收录刊物：SCIE、ISTIC、Scopus

卷号：57

期号：6

页面范围：1012-1022

ISSN号：0253-6102

关键字：Lie algebra; integrable system; elliptic variable solution

摘要：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.