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:
-
10%
-
20%
-
30%
-
40%
-
50%