Caudrey–Dodd–Gibbon–Kotera–Sawada方程的对称、精确解和守恒律

J4 ›› 2011, Vol. 28 ›› Issue (4): 385-390.

• 量子物理 • 下一篇

Caudrey–Dodd–Gibbon–Kotera–Sawada方程的对称、精确解和守恒律

王婷婷,刘希强,于金倩

聊城大学数学科学学院，山东聊城 252059

收稿日期:2010-09-25 修回日期:2010-11-20 出版日期:2011-07-28 发布日期:2011-07-06
通讯作者: 刘希强（1957-）山东菏泽人，教授，博士。研究方向为非线性微分方程系统。
作者简介:王婷婷（1986-），女，山东德州人，研究生。研究方向为偏微分方程理论及其应用。Email：wangting860108@163.com
基金资助:
国家自然科学基金与中物院联合基金资助项目（11076015），山东省自然科学基金资助项目( 2008A35)

Symmetries, exact solutions and conservation laws of Caudrey–Dodd–Gibbon–Kotera–Sawada equation

WANG Ting-ting, LIU Xi-qiang, YU Jin-qian

School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China

Received:2010-09-25 Revised:2010-11-20 Published:2011-07-28 Online:2011-07-06

摘要/Abstract

摘要：

应用改进的CK直接方法，得到了（2+1）维Caudrey–Dodd–Gibbon–Kotera–Sawada（CDGKS）方程的对称群定理。利用对称群理论和方程的旧解得到了该方程新的精确解，扩大了解的范围。最后根据对称和共轭方程求出了（2+1）维CDGKS方程的无穷多守恒律。

关键词: （2+1）维CDGKS方程, 改进的CK直接方法, 精确解, 守恒律

Abstract:

By using the improved CK´s, the symmetry group theorem (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation was derived. Some new exact solutions of (2+1)-dimensional CDGKS equation are obtained by applying our theorem and given solutions, which expands the scope of the solutions of CDGKS equation. Infinite conservation laws of (2+1)-dimensional CDGKS equation are also found by symmetries and the adjoint equation.

Key words: (2+1)-dimensional CDGKS equation, improved CK´s, exact solutions, conservation laws

中图分类号:

O175.2

王婷婷刘希强于金倩. Caudrey–Dodd–Gibbon–Kotera–Sawada方程的对称、精确解和守恒律[J]. J4, 2011, 28(4): 385-390.

WANG Ting-ting, LIU Xi-qiang, YU Jin-qian. Symmetries, exact solutions and conservation laws of Caudrey–Dodd–Gibbon–Kotera–Sawada equation[J]. J4, 2011, 28(4): 385-390.

参考文献

[1] Konopelchenko, B., Dubrovsky, V.. Some new integrable evolution equations in 2+1 dimensions [J]. Phys. Lett. A, 1984, 102: 15-17.
[2] Yi Cheng, Yi-Shen Li. J. Phys. Constraints of the 2+1 dimensional integrable soliton systems [J]. J. Phys. A: Math. Gen., 1992, 25: 419.
[3] Chan W. L., Zheng Yu-Kun. Backlund transformations for the Caudrey–Dodd–Gibbon–Kotera–
Sawada equation and itsλ-modified equation [J]. J. Math. Phys., 1989, 30; 2065-2068.
[4] Cao Ce-wen, Wu Yong-tang, Geng Xian-guo. On quasi-periodic solutions of the 2+1 dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation [J]. Phys. Lett. A, 1999, 256: 59–65.
[5] Lv Na, Mei Jian-Qin, Zhang Hong-Qing. Symmetry Reductions and Group-Invariant Solutions of (2+1)-Dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada Equation [J]. Commun. Theor. Phys., 2010, 53: 591-596.
[6] J.D. Gibbon, R.K. Dodd, P.J. Caudrey. A new hierarchy of Kortewge-de Vries equations [J]. Proc. Roy. Soc. Lond. Ser. A., 1976, 351: 407-422.
[7] R.K. Dodd, J.D. Gibbon. The prolongation structure of a higher order Kortewge-de Vries equations [J]. Proc. Roy. Soc. Lond. Ser. A., 1977, 358: 287-296.
[8] Lou Sen-Yue, Ma Hong-Cai. Non-Lie symmetry groups of (2+1) –dimensional nonlinear systems obtained form a simple direct method [J]. J. Phys A: Math. Gen. 2005, 38: L129~L137.
[9] Gao Jie, Liu Xi-Qiang, Guo Mei-Yu. New solutions and conservation lows of the (3+1)-dimensional nonlinear evolution equations [J]. Chinese Journal of Quantum Electronics(量子电子学报), 2009, (1): 16-22 (in Chinese).
[10] Yang Zong-Hang. A Series of Exact Solutions of (2+1)-Dimensional CDGKS Equation [J]. Commun. Theor. Phys., 2006, 46: 807-811.
[11] Xu Bin, Liu Xi-Qiang. Symmetry reduction and invariable solutions of the (2+1)-dimensional Gardner equation [J]. Chinese Journal of Quantum Electronics(量子电子学报). 2009, 26(5): 531-536(in Chinese).
[12] Nail H I. A new conservation theorem [J]. J. Math. Anal. Appl., 2007, 333: 311~328.

[1]	马志民1，*，孙峪怀2，. 立方非线性Schr\"{o}dinger方程新精确解[J]. 量子电子学报, 2019, 36(4): 416-422.
[2]	张立华赵琳琳刘希强. 多孔介质中自然对流Brinkman模型的新精确解[J]. J4, 2017, 34(6): 691-699.
[3]	王晓利斯仁道尔吉. Exp-展开法与变系数非线性发展方程的精确解[J]. J4, 2016, 33(6): 680-688.
[4]	李康，刘希强. 广义变系数Kuramoto-Sivashinsky方程的显式解[J]. J4, 2015, 32(4): 419-424.
[5]	靳玲花庞晶. 变形Boussinesq方程组II的推广解[J]. J4, 2015, 32(4): 425-430.
[6]	冯春明，刘庆松. 含色散项的Zabolotskaya-Khokhlov方程的对称、约化、精确解和守恒律[J]. J4, 2015, 32(1): 46-52.
[7]	于兴江. （3+1）维广义KdV-Zakharov-Kuznetsev方程的对称、约化和精确解[J]. J4, 2014, 31(6): 670-677.
[8]	刘勇刘希强王振立. (2+1)维Potential Boiti-Leon-Manna-Pempinelli方程的对称、约化和精确解 [J]. J4, 2014, 31(5): 533-540.
[9]	王振立, 刘希强. 广义四阶色散方程的对称约化和精确解[J]. J4, 2014, 31(3): 264-272.
[10]	康晓蓉,鲜大权. (2+1)维AKNS方程的对称约化和新的非行波精确解[J]. J4, 2013, 30(6): 678-683.
[11]	张立华. 带强迫项的KdV方程的非线性自伴随性和守恒律[J]. J4, 2013, 30(2): 154-161.
[12]	邱春刁明军徐兰兰岳书波赵静. 构造非线性演化方程精确解的一个新方法[J]. J4, 2012, 29(3): 279-285.
[13]	韩元春额尔敦仓那仁满都拉. 变系数（2+1）维Burgers系统的精确解及特殊孤波结构[J]. J4, 2012, 29(3): 286-291.
[14]	杨立娟杨琼芬杜先云. Broer–Kaup–Kupershmidt方程的新精确解[J]. J4, 2012, 29(2): 142-146.
[15]	陈美, 刘希强, 王猛. 对称正则长波方程组的对称,精确解和守恒律[J]. J4, 2012, 29(1): 21-26.

Caudrey–Dodd–Gibbon–Kotera–Sawada方程的对称、精确解和守恒律

Symmetries, exact solutions and conservation laws of Caudrey–Dodd–Gibbon–Kotera–Sawada equation

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价