Lie Point Symmetries of Differential-Difference Equations
Lie Point Symmetries of Differential-Difference Equations
摘要
In this paper, the classical Lie group approach is extended to find some Lie point symmetries of differentialdifference equations. It reveals that the obtained Lie point symmetries can constitute a Kac-Moody-Virasoro algebra.
基金
国家杰出青年科学基金,国家自然科学基金,高等学校博士学科点专项科研项目
参考文献10
-
1[1]Ed. P.J. Olver, Applications of Lie Group to Differential Equations, 2nd ed., Graduate Texts Math., Springer, New York (1993) 107; G.W. Bluman and J.D. Cole, J. Math.Mech. 18 (1969) 1025; G.W. Bluman and S. Kumei, Symmetries and Differential Equation, Springer, New York (1989).
-
2[2]D. Levi and P. Winternitz, Phys. Lett. A152 (1991) 335.
-
3[3]D. Levi and P. Winternitz, J. Math. Phys. 34 (1993) 3713.
-
4[4]D. Levi and P. Winternitz, J. Math. Phys. 37 (1996)5551; D. Gomez-Ullate, S. Lafortune, and P. Winternitz,J. Math. Phys. 40 (1999) 2782; V. Dorodnitsyn, R. Kozlov, and P. Winternitz, J. Math. Phys. 41 (2000) 480;S. Lafortune, S. Tremblay, and P. Winternitz, J. Math.Phys. 42 (2001) 5341.
-
5[5]G.R.W. Quispel, H.W. Capel, and R. Sahadevan, Phys.Lett. A170 (1992) 379.
-
6[6]C.R. Gilson, X.B. Hu, W.X. Ma, and H.W. Tam, Physica D175 (2003) 177.
-
7[7]S.Y. Lou, J. Math. Phys. 41 (2000) 6509; X.Y. Tang and S.Y. Lou, Chin. Phys. Lett. 19 (2002) 1.
-
8[8]H.W. Tam, X.B. Hu, and X.M. Qian, J. Math. Phys. 43(2002) 1008.
-
9[9]K.M. Tamizhmani, S. Kanagavel, B. Grammaticos, and A. Rimani, Chaos, Solitons, and Fractals 11 (2000) 1423.
-
10[10]X.Y. Tang, X.M. Qian, and W. Ding, "A General Differential-Difference Kadomtsev-Petviashvili Family with a Common Kac-Moody-Virasoro Symmetry Algebra",preprint.
-
1亓欢歌,程永胜,王梦平,武琳丽.Kac Determinant Formula for the q-deformed Virasoro Algebra of Hom-type[J].Chinese Quarterly Journal of Mathematics,2016,31(4):331-339. 被引量:1
-
2Qifen Jiang,Song Wang.Derivations and Automorphism Group of Original Deformative Schrodinger-Virasoro Algebra[J].Algebra Colloquium,2015,22(3):517-540. 被引量:2
-
3王竑,徐兆新,查朝征.A NEW EXTENSION OF THE HIGH-ORDER VIRASORO ALGEBRA[J].Acta Mathematica Scientia,2001,21(3):302-306.
-
4高芳,张晓波,傅景礼.Application of canonical coordinates for solving single-freedom constraint mechanical systems[J].Applied Mathematics and Mechanics(English Edition),2014,35(8):1029-1038. 被引量:1
-
5Shunzhou WU,Xiumin ZHENG.Growth of Meromorphic Solutions of Complex Linear Differential-Difference Equations with Coefficients Having the Same Order[J].Journal of Mathematical Research with Applications,2014,34(6):683-695. 被引量:1
-
6李玉奇,陈俊超,陈勇,楼森岳.Darboux Transformations via Lie Point Symmetries: KdV Equation[J].Chinese Physics Letters,2014,31(1):1-4. 被引量:2
-
7徐西祥.Bargmann Symmetry Constraint for a Family of Liouville Integrable Differential-Difference Equations[J].Communications in Theoretical Physics,2012,57(6):953-960. 被引量:1
-
8王鑫,陈勇,董仲周.Symmetries and conservation laws of one Blaszak-Marciniak four-field lattice equation[J].Chinese Physics B,2014,23(1):35-40. 被引量:1
-
9罗琳,范恩贵.A Hierarchy of Differential-Difference Equations and Their Integrable Couplings[J].Chinese Physics Letters,2007,24(6):1444-1447. 被引量:1
-
10Haichou LI.Some Properties of Meromorphic Solutions to Systems of Complex Differential-Difference Equations[J].Chinese Annals of Mathematics,Series B,2016,37(5):719-728.