基于Lamé方程和新的Lamé函数,应用摄动方法和Jacobi椭圆函数展开法求解了立方非线性薛定谔方程,获得多种新的多级准确解.这些解对应着不同形式的包络周期解.这些解在极限条件下可以退化为各种形式的包络孤波解.这表明利用Jacobi椭圆函数和Lamé方程,在符号计算的帮助下,可获得若干非线性发展方程的多级渐进周期解.
参考文献
| [1] | Miura M R.B(a)cklund Transformation[M].Berlin:Springer-Verlag,1978. |
| [2] | Gu Chaohao,Hu Hesheng,et al..Darboux Transformation in Solitons Theory and Geometry Applications (孤立子理论中的达布变换及其几何应用)[M].Shanghai:Shanghai Science Technology Press,1999 (in Chinese). |
| [3] | Hirota R.Exact solution of the Korteweg-de Vries for multiple collisions of solutions[J].Phys.Rev.Lett.,1971,27:1192-1194. |
| [4] | Wang Mingliang.Solitary wave solutions for variant Boussinesq equations[J].Phys.Lett.A,1996,199:169-172. |
| [5] | Wang Mingliang,Zhou Yubin,Li Zhibin.Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics[J].Phys.Lett.A,1996,216:67-75. |
| [6] | Weiss J,Tabor M,Carnevale G.The Painnlevé property for partial differential equations[J].J.Math.Phys.,1983,24:552-564. |
| [7] | Liu Shikuo,Liu Shida.Nonlinear Equations of Physics (物理学中的非线性方程)[M].Beijing:Beijing University Press,2000 (in Chinese). |
| [8] | Nayfeh A H.Perturbation Methods[M].New York:John Wiley and Sons Inc.,1973. |
| [9] | Liu Shikuo,Fu Zuntao,Liu Shida,et al.Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations[J].Phys.Lett.A,2001,289:69-74. |
| [10] | Fu Zuntao,Liu Shikuo,Liu Shida,et al.The JEFE method and periodic solutions of two kinds of nonlinear wave equations[J].Commu.Nonlinear.Sci.Simul.,2003,8:67-75. |
| [11] | Xiao Yafeng,Zhang Hongqing.Solutions of modified improved Boussinesq equation with extended elliptic function expansion[J].Journal of Lanzhou University of Technology (兰州理工大学学报),2004,30(1):9-12 (in Chinese). |
| [12] | Yan Zhenya.The extended Jacobian elliptic functions expansion method and its application in the generalized Hirota-Satsuma coupled KdV systems[J].Chaos,Solitons and Fractals,2003,15(3):575-583. |
| [13] | Tian Guichen,Liu Xiqiang.Exact solutions of the general variable coefficient KdV equation with external force term[J].Chinese Journal of Quantum Electronics (量子电子学报),2005,22:339-343 (in Chinese). |
| [14] | Zheng Bin.New soliton solutions to (2+1)-dimensional breaking soliton equation[J].Chinese Journal of Quantum Electronics (量子电子学报),2006,23:451-455 (in Chinese). |
| [15] | Liu Na,Liu Xiqiang.Symmetries,new exact solutions and conservation laws of (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation[J].Chinese Journal of Quantum Electronics (量子电子学报),2008,25(5):546-552 (in Chinese). |
| [16] | Taogetusang,Sirendaoerji.Jacobi elliptic function exact solutions of sine-Gordon equation[J].Chinese Journal of Quantum Electronics (量子电子学报),2009,26(3):278-287 (in Chinese). |
| [17] | Liu Shikuo,Fu Zuntao,Liu Shida,et al.Lamé equation and multi-order exact solutions to nonlinear evolution equations[J].Chaos,Soliton and Fractals,2004,19:795-801. |
| [18] | Liu Shikuo,Chen Hua.,Fu Zuntao,et al.Lamé function and invariants of multi-order exact solutions among nonlinear evolution equations[J].Acta Physica Sinica (物理学报),2003,52(8):1842-1847 (in Chinese). |
| [19] | Fu Zuntao,Liu Shikuo,Liu Shida.New multi-order exact solutions to a kind of nonlinear evolution equations[J].Acts Physica Sinica (物理学报),2003,52(12):2949-2953 (in Chinese). |
| [20] | Fu Zuntao,Yuan Naiming,et al.Multi-order exact solutions to the Drinfel,d-Sokolov-Wilson equations[J].Phys.Lett.A,2009,373:3710-3714. |
| [21] | Fu Zuntao,Yuan Naiming,et al.New Lamé equation and its application to nonlinear equations[J].Phys.Lett.A,2009,374:214-217. |
| [22] | Wang Zhuxi,Guo Dunren.Special Functions[M].Singapore:World Scientific Press,1989. |
| [23] | Fan Engui.Extended tanh-function method and its application to nonlinear equation[J].Phys.Lett.A,2000,277:212-218. |
| [24] | Kudryashov N A.Exact solutions of the generalized Kuramoto-Sivashinsky equation[J].Phys.Lett.A,1990,147:287-291. |
| [25] | Yan Chuntao.A simple transformation for nonlinear waves[J].Phys.Lett.A,1996,224:77-84. |
| [26] | Dong Zhongzhou,Yu Xichang,et al.Exact travelling wave solutions of the nonlinear coupled KdV equations[J].Chinese Journal of Quantum Electronics (量子电子学报),2006,23:31-34 (in Chinese). |
| [27] | Xiang Chunhua,Wang Honglei.Complex traveling wave solution to the Gross-Pitaevskii equation[J].Chinese Journal of Quantum Electronics (量子电子学报),2008,25(3):151-154(in Chinese). |
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%