The simple Lie point symmetry reduction procedure is used to obtain infinitely many symmetries to a new integrable system of coupled KdV equations. Using some symmetry subalgebra of the equations, five types of the si...The simple Lie point symmetry reduction procedure is used to obtain infinitely many symmetries to a new integrable system of coupled KdV equations. Using some symmetry subalgebra of the equations, five types of the significant similarity reductions are obtained by virtue of the Lie group approach, and obtain abundant solutions of the coupled KdV equations, such as the solitary wave solution, exponential solution, rational solution, polynomial solution, etc.展开更多
There have been a great many of studies on the pointed representations of fi- nite-dimensional sanple Lie algebras.cf.[1][2]etc.In this paper we give a new proof of an impottant Lemma,and from this we derive our main ...There have been a great many of studies on the pointed representations of fi- nite-dimensional sanple Lie algebras.cf.[1][2]etc.In this paper we give a new proof of an impottant Lemma,and from this we derive our main result:Irreducible pointed modules of finite -dimesional simple Lie algebras are all Harish-Chandra modules.展开更多
By use of a direct method, we discuss symmetries and reductions of the two-dimensional Burgers equation with variable coefficient (VCBurgers). Five types of symmetry-reducing VCBurgers to (1+1)-dimensional partial dif...By use of a direct method, we discuss symmetries and reductions of the two-dimensional Burgers equation with variable coefficient (VCBurgers). Five types of symmetry-reducing VCBurgers to (1+1)-dimensional partial differential equation and three types of symmetry reducing VCBurgers to ordinary differential equation are obtained.展开更多
For a graded simple Lie algebra of Cartan type L=X(m:n) (2) X∈{W,S,H,K} , over a field F of odd characteristic p , the group generated by one-parameter subgroups of the form exp( t ad y )is descr...For a graded simple Lie algebra of Cartan type L=X(m:n) (2) X∈{W,S,H,K} , over a field F of odd characteristic p , the group generated by one-parameter subgroups of the form exp( t ad y )is described, where y∈L+F u satisfying y p=0 , t∈F and u is some fixed element of the p -envelope of L in Der u (m :n).展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10071033 and the Natural Science Foundation of Jiangsu Province under Grant No. BK2002003. Acknowledgments 0ne of the authors （S.P. Qian） is indebted to Prof. S.Y. Lou for his helpful discussions.
文摘The simple Lie point symmetry reduction procedure is used to obtain infinitely many symmetries to a new integrable system of coupled KdV equations. Using some symmetry subalgebra of the equations, five types of the significant similarity reductions are obtained by virtue of the Lie group approach, and obtain abundant solutions of the coupled KdV equations, such as the solitary wave solution, exponential solution, rational solution, polynomial solution, etc.
文摘There have been a great many of studies on the pointed representations of fi- nite-dimensional sanple Lie algebras.cf.[1][2]etc.In this paper we give a new proof of an impottant Lemma,and from this we derive our main result:Irreducible pointed modules of finite -dimesional simple Lie algebras are all Harish-Chandra modules.
文摘By use of a direct method, we discuss symmetries and reductions of the two-dimensional Burgers equation with variable coefficient (VCBurgers). Five types of symmetry-reducing VCBurgers to (1+1)-dimensional partial differential equation and three types of symmetry reducing VCBurgers to ordinary differential equation are obtained.
文摘For a graded simple Lie algebra of Cartan type L=X(m:n) (2) X∈{W,S,H,K} , over a field F of odd characteristic p , the group generated by one-parameter subgroups of the form exp( t ad y )is described, where y∈L+F u satisfying y p=0 , t∈F and u is some fixed element of the p -envelope of L in Der u (m :n).
