一个(3+1)维非线性偏微分方程的有限对称变换群和精确解
PDF下载 (419)王美丽,李 彪 *.一个(3+1)维非线性偏微分方程的有限对称变换群和精确解[J].宁波大学学报(理工版),2015,28(04):96-99.DOI:
WANG Mei-li,LI Biao *.Finite Symmetry Transformation Groups and Some Exact Solutions of a (3+1)-dimensional Nonlinear Evolution Equation[J].Journal of Ningbo University(Natural Science & Engineering Edition),2015,28(04):96-99.DOI:
| Title: | Finite Symmetry Transformation Groups and Some Exact Solutions of a (3+1)-dimensional Nonlinear Evolution Equation |
| 作者: | 王美丽, 李 彪 * |
| Author(s): | WANG Mei-li, LI Biao * |
| 关键词: | 对称群; 精确解; 符号计算; (3+1)维 方程; 广义射影 展开法 |
| Keywords: | symmetry groups; exact solutions; symbolic computation; (3+1)-dimensional NEE equation; the projective Riccati expansion method |
| 分类号: | O175.29 |
| 文献标识码: | A |
| 摘要: | 基于符号计算与对称群直接法研究了一个(3+1)维非线性偏微分方程 的对称群与精确解, 获得该方程的李点对称群和非李对称群. 最后通过广义射影 展开法研究方程的精确解, 并由获得的有限对称变换群构造了相应新的一般解. |
| Abstract: | Based on symbolic computation and the symmetry group direct method, we investigate symmetry groups and exact solution of a (3+1)-dimensional nonlinear evolution equation , both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. Finally, using a generalized sub-equation expansion method, some exact solutions of the (3+1)-dimensional nonlinear evolution equation are derived, and the corresponding new solutions can be constructed through the finite symmetry transformation groups obtained. |
| 参考文献 /References: | [1] Bluman G W, Cole J D. Similarity methods for differ- rential equations[M]. New York: Springer Presses, 1974: 88-95. [2] Olver P J, Rosenau P. Group-invariant solutions of differential equations[J]. Phys Lett A, 1986, 114:107-112. [3] Tian C. Lie Group and its applications in differential equations[M]. Beijing: Science Press, 2001:96-104. [4] Olver P J. Applications of Lie Groups to Differential Equations[M]. 2nd ed. New York: Springer Presses, 1993: 55-71. [5] Bluman G W, Kumei S. Symmetries and differential equations[M]. Berlin: Springer Verlag Presses, 1989:2-15. [6] Clarkson P A, Kruskal M D, New similarity reductions of the Boussinesq equation[J]. J Math Phys, 1989, 30:2201- 2213. [7] Clarkson P A. New similarity solutions for the modified Boussinesq equation[J]. J Phys A: Math Gen, 1989, 22 (13):2355-2367. [8] Lou Senyue. Symmetries and similarity reductions of the Dym equation[J]. Phys Scr, 1996, 54:428-435. [9] Lou Senyue, Ruan Hangyu, Chen Defang, et al. Similarity reductions of the KP equation by a direct method[J]. J Phys A, 1991, 24:1455-1458. [10] Lou Senyue, Ma Hongcai. Non-lie symmetry groups of (2+1)-dimensional nonlinear systems obtained from a simple direct method[J]. J Phys A: Math Gen, 2005, 38: 129-137. [11] Ma Hongcai, Lou Senyue. Finite symmetry transforma- tion groups and exact solutions of Lax integrable systems [J]. Chin Phys B, 2005, 14(8):1495-1500. [12] Geng X G. Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations[J]. J Phys A, 2003, 36:2289-2303. [13] Geng Xianguo, Ma Yunling. N-soliton solution and its Wronskian form of a (3+1)-dimensional nonlinear evolution equation [J]. Phys Lett A. 2007, 369:285-289. [14] Zha Qilao, Li Zhibin. Darboux transformation and various solutions for a nonlinear evolution equation in (3+1)-dimensions[J]. Mod Phys Lett B, 2008, 22:2945- 2966. [15] Zha Qilao. Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation[J]. Phys Lett A, 2013, 377:3021-3026. [16] Li Biao, Chen Yong. On exact solutions of the nonlinear Schr?dinger equations[J]. Chaos, Solitons and Fractals, 2004, 21:241-247. |
| 备注/Memo: | 收稿日期: 2014-03-24. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（11271211）. 第一作者: 王美丽（1986－）, 女, 河北廊坊人, 在读硕士研究生, 主要研究方向: 非线性偏微分方程. E-mail: fengli0210ai@163.com *通信作者: 李彪（1971－）, 男, 湖南会同人, 教授, 主要研究方向: 数学物理与数学机械化. E-mail: libiao@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
