A 3 × 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 e...A 3 × 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 Schro¨dinger 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 × 3 Lie subalgebra into a 2 × 2 matrix Lie algebra.Finally,we discuss the elliptic variable solutions of a generalized BK equation.展开更多
基金Supported by Natural Science Foundation of Liaoning Province under Grant No. 20092171
文摘A 3 × 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 Schro¨dinger 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 × 3 Lie subalgebra into a 2 × 2 matrix Lie algebra.Finally,we discuss the elliptic variable solutions of a generalized BK equation.
