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利用经典李群方法,得到了一类(2+1)维Gardner方程的显式解,推广了唐和陈的某些结果,并且得到了该方程的对称、约化及其群不变解.

参考文献

[1] Zheng Bin.New soliton solutions to (2+l)-dimensional breaking soliton equation[J].Chinese Journal of Quantum Electronics (量子电子学报),2006,23:451-455 (in Chinese).
[2] Liu Xiqiang.New explicit solutions of the (2+1)-dimensional Broer-Kaup equations[J].J.Partial Diff.Eqs.,2004,17:1-9.
[3] 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).
[4] Fan Engui,Zhang Jian.Applications of the Jacobi elliptic function method to special-type nonlinear eqations[J].Phys.Lett.A,2002,305:383-392.
[5] 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).
[6] Liu Xiqiang,Jiang Song.The sechq-tanq-method and its application[J].Phys.Lett.A,2002,298:253-258.
[7] Li Fuzhi,Liu Xiqiang.Symmetry reduction and invariable solutions of the Jimbo-Miwa equation[J].Chinese Journal of Quantum Electronics (量子电子学报),2008,25:155-160.
[8] Yan Zhilian,Liu Xiqiang.Symmetry reduction and explicit solutions for a generalized Zakharov-Kuznetsov equation[J].Commun.Theor.Phys.,2006,45:29-32.
[9] Tang Yaning,Xu Wei,Shen Jianwei.Solitary wave solution to Gardner equation[J].Chinese Journal of Engineering Mathematics,2007,24(1):119-127.
[10] Fu Zuntao,Liu Shida,Liu Shikuo.New kinds of solutions to Gardner equation[J].Chaos,Solitons and Fraetals,2004,20:301-309.
[11] Abdul-Majid Wazwaz.New solitons and kink solutions for the Gardner equation[J].Communications in Nonlinear Science and Numerical Simulation,2007,12:1395-1404.
[12] Chen Yong,Yah Zhenya.New exact solutions of (2+1)-dimensional Gardner equation via the new sine-Gordon equation expansion method[J].Chaos,Solitons and Fractals,2005,26:399-406.
[13] Tian Chou.Applications of Lie Group Method to Partial Differential Equation (李群及其在微分方程中的应用)[M].Beijing:Science and Technology Press,2001.248-268 (in Chinese).
[14] Liu Shikuo,Liu Shida.Nonlinear Equations of Physics (物理学中的非线性方程)[M].Beijing:Beijing University Press,2000.32-53 (in Chinese).
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