欢迎登录材料期刊网

材料期刊网

高级检索

基于推广的对称群方法和符号计算,一些变系数非线性薛定谔方程的有限对称群解得到了研究.在推广对称群的基础上,对超定方程组分3种情况讨论,构造6种对称变换,并推导出标准的(3+1)-维非线性薛定谔方程和(3+1)-维变系数非线性薛定谔方程之间的关系.利用对称变换,从标准的(3+1)-、维非线性薛定谔方程解中得到了(3+1)-维变系数非线性薛定谔方程丰富的精确解.

参考文献

[1] 徐四六;陈顺芳;孙运周.变系数(2+1)维非线性薛定谔方程中奇异结构孤子[J].量子电子学报,2013(3):335-340.
[2] 肖亚峰;薛海丽;张鸿庆.立方非线性薛定谔方程的新多级包络周期解[J].量子电子学报,2012(3):269-278.
[3] 靳海芹;易林;蔡泽彬.二维谐振子调制势中光束传输特性研究[J].量子电子学报,2013(3):323-329.
[4] Li Hua-Mei.Exact self-similar solitary waves and collisions in nonlinear optical media[J].中国物理B(英文版),2008(3):759-763.
[5] Huang Guo-Xiang.Second harmonic generation of propagating collective excitations in Bose-Einstein condensates[J].中国物理(英文版),2004(11):1866-1876.
[6] Lv Zhong-Quan;Zhang Lu-Ming;Wang Yu-Shun.A conservative Fourier pseudospectral algorithm for the nonlinear Schr(o)dinger equation[J].中国物理B(英文版),2014(12):21-29.
[7] Jiang Chao-Long;Sun Jian-Qiang.A high order energy preserving scheme for the strongly coupled nonlinear Schr(o)dinger system[J].中国物理B(英文版),2014(5):36-40.
[8] Yin Jiu-Li;Zhao Liu-Wei;Tian Li-Xin.Chaos control in the nonlinear Schr(o)dinger equation with Kerr law nonlinearity[J].中国物理B(英文版),2014(2):44-48.
[9] Wang Jia;Li Biao.Symmetry and general symmetry groups of the coupled Kadomtsev-Petviashvili equation[J].中国物理B(英文版),2009(6):2109-2114.
[10] Yao Ruo-Xia;Jiao Xiao-Yu;Lou Sen-Yue.Infinite series symmetry reduction solutions to the modified KdV-Burgers equation[J].中国物理B(英文版),2009(5):1821-1827.
[11] Jia Man.Lie point symmetry algebras and finite transformation groups of the general Broer-Kaup system[J].中国物理(英文版),2007(6):1534-1544.
[12] Ma Hong-Cai;Lou Sen-Yue.Finite symmetry transformation groups and exact solutions of Lax integrable systems[J].中国物理(英文版),2005(8):1495-1500.
[13] Li Jin-Hua;Lou Sen-Yue.Kac-Moody-Virasoro symmetry algebra of a (2+1)-dimensional bilinear system[J].中国物理B(英文版),2008(3):747-753.
[14] Lian Zeng-Ju;Chen Li-Li;Lou Sen-Yue.Painlevé property, symmetries and symmetry reductions of the coupled Burgers system[J].中国物理(英文版),2005(8):1486-1494.
[15] Elizabeth L. Mansfield;Gregory J. Reid;Peter A. Clarkson.Nonclassical reductions of a 3+1-cubic nonlinear Schrodinger system[J].Computer physics communications,19982/3(2/3):460-488.
[16] LI Biao;LI Yu-Qi;CHEN Yong.Finite Symmetry Transformation Groups and Some Exact Solutions to (2+1)-Dimensional Cubic Nonlinear Schr(o)dinger Equantion[J].理论物理通讯(英文版),2009(5):773-776.
[17] Wang Jia;Li Biao;Ye Wang-Chuan.Approximate solution for the Klein-Gordon-Schr(o)dinger equation by the homotopy analysis method[J].中国物理B(英文版),2010(3):83-89.
[18] Wang Huan;Li Biao.Solitons for a generalized variable-coefficient nonlinear Schr(o)dinger equation[J].中国物理B(英文版),2011(4):8-15.
[19] Hu Xiao;Li Biao.Exact analytical solutions of three-dimensional Gross Pitaevskii equation with time-space modulation[J].中国物理B(英文版),2011(5):122-129.
[20] Li B;Zhang XF;Li YQ;Chen Y;Liu WM.Solitons in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic and complex potential[J].Physical Review, A,20082 Pt.b(2 Pt.b):023608-1-023608-6-0.
[21] Jing Jian-Chun;Li Biao.Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schr(o)dinger equation with variable coefficients[J].中国物理B(英文版),2013(1):77-83.
[22] Camassa R.;Luce BP.;Hyman JM..Nonlinear waves and solitons in physical systems[J].Physica, D. Nonlinear phenomena,19981/4(1/4):1-20.
[23] Ruan HY;Li HJ;Chen YX.Exact solutions of space-time dependent non-linear Schrodinger equations[J].Mathematical Methods in the Applied Sciences,20049(9):1077-1087.
[24] RUAN HangYu;Chen Yixin;LOU SenYue.General Symmetry Approach to Solve Variable-Coefficient Nonlinear Equations[J].理论物理通讯(英文版),2001(06):641-646.
[25] Ruan HY;Li HJ;Chen YX.The application of the extending symmetry group approach in optical soliton communication[J].Journal of Physics.A.Mathematical and General:A Europhysics Journal,200518(18):3995-4008.
[26] Li Zhi-Fang;Ruan Hang-Yu.The extended symmetry approach for studying the general Korteweg-de Vries-type equation[J].中国物理B(英文版),2010(4):1-8.
上一张 下一张
上一张 下一张
计量
  • 下载量()
  • 访问量()
文章评分
  • 您的评分:
  • 1
    0%
  • 2
    0%
  • 3
    0%
  • 4
    0%
  • 5
    0%