The inhomogeneous nonlinear difusion equation is studied by invariant subspace and conditional Lie-Bcklund symmetry methods.It is shown that the equations admit a class of invariant subspaces governed by the nonlinear...The inhomogeneous nonlinear difusion equation is studied by invariant subspace and conditional Lie-Bcklund symmetry methods.It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary diferential equations,which is equivalent to a kind of higher-order conditional Lie-Bcklund symmetries of the equations.As a consequence,a number of new solutions to the inhomogeneous nonlinear difusion equations are constructed explicitly or reduced to solving fnite-dimensional dynamical systems.展开更多
We study conformal biderivations of a Lie conformal algebra.First,we give the definition of a conformal biderivation.Next,we determine the conformal biderivations of loop W(a,b)Lie conformal algebra,loop Virasoro Lie ...We study conformal biderivations of a Lie conformal algebra.First,we give the definition of a conformal biderivation.Next,we determine the conformal biderivations of loop W(a,b)Lie conformal algebra,loop Virasoro Lie conformal algebra,and Virasoro Lie conformal algebra.Especially,all conformal biderivations on Virasoro Lie conformal algebra are inner conformal biderivations.展开更多
For any complex parameters a, b, let W（a, b） be the Lie algebra with basis {Li, Hi｜i ∈ Z} and relations [Li,Lj] = （j - i）Li＋j, [Li,Hj] = （a ＋ j ＋ bi）Hi＋j and [Hi, Hi] = 0. In this paper, we construct the W...For any complex parameters a, b, let W（a, b） be the Lie algebra with basis {Li, Hi｜i ∈ Z} and relations [Li,Lj] = （j - i）Li＋j, [Li,Hj] = （a ＋ j ＋ bi）Hi＋j and [Hi, Hi] = 0. In this paper, we construct the W（a, b） conformal algebra for some a, b and its conformal module of rank one.展开更多
基金Supported by National Natural Science Foundation of China(11971315,11871249)Scientific Research Project of Huzhou University(The structures and representations of several types of infinite dimensional Lie algebras)
基金supported by National Natural Science Foundation of China for Distinguished Young Scholars(Grant No.10925104)the PhD Programs Foundation of Ministry of Education of China(Grant No.20106101110008)the United Funds of NSFC and Henan for Talent Training(Grant No.U1204104)
文摘The inhomogeneous nonlinear difusion equation is studied by invariant subspace and conditional Lie-Bcklund symmetry methods.It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary diferential equations,which is equivalent to a kind of higher-order conditional Lie-Bcklund symmetries of the equations.As a consequence,a number of new solutions to the inhomogeneous nonlinear difusion equations are constructed explicitly or reduced to solving fnite-dimensional dynamical systems.
基金supported by the National Natural Science Foundation of China(Grant Nos.11771069,12071405,11301109)China Postdoctoral Science Foundation(2020M682272)the Natural Science Foundation of Hennan Province(212300410120).
文摘We study conformal biderivations of a Lie conformal algebra.First,we give the definition of a conformal biderivation.Next,we determine the conformal biderivations of loop W(a,b)Lie conformal algebra,loop Virasoro Lie conformal algebra,and Virasoro Lie conformal algebra.Especially,all conformal biderivations on Virasoro Lie conformal algebra are inner conformal biderivations.
文摘For any complex parameters a, b, let W（a, b） be the Lie algebra with basis {Li, Hi｜i ∈ Z} and relations [Li,Lj] = （j - i）Li＋j, [Li,Hj] = （a ＋ j ＋ bi）Hi＋j and [Hi, Hi] = 0. In this paper, we construct the W（a, b） conformal algebra for some a, b and its conformal module of rank one.
