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应用试探函数方法求解了mBBM方程和Vakhnenko方程.通过引入试探函数,把难于求解的非线性偏微分方程化为易于求解的代数方程,然后用待定系数法确定相应的常数,从而简洁地求得方程的精确解.

参考文献

[1] Ablowitz M J,Clarkson P A.Soliton,Nonlinear Evolution Equations and Inverse Scattering[M].New York:Cambridge University Press,1991.
[2] Hasegawa A.Optical Solitons in Fibers[M].Berlin:Springer,1989.
[3] 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(4):451-455(in Chinese).
[4] 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(3):339-343(in Chinese).
[5] Taogetusang,Sirendaoerji.Jacobi-like elliptic function exact solutions of(3+1)-dimensional Zakharov-Kuznetsov equation[J].Chinese Journal of Quantum Electronics(量子电子学报),2010,27(1):6-14(in Chinese).
[6] Taogetusang,Sirendaoerji.New solitary wave solutions of the combined KdV equation with the variable coefficients[J].Chinese Journal of Quantum Electronics(量子电子学报),2009,26(2):148-154(in Chinese).
[7] Li Bangqing,Ma Yulan,Xu Meiping.(G'/G)-expansion method and novel fractal structures for high-dimensional nonlinear physical equation[J].Acta Physica Sinica(物理学报),2010,59(3):1409-1415(in Chinese).
[8] Xie Yuanxi,Tang Jiashi.New solitary wave solutions to the KdV-Burgers equation[J].International Journal of Theoretical Physics,2005,44(3):304-312.
[9] Xie Yuanxi,Tang Jiashi.A simple fast method in finding the analytical solutions of a class of nonlinear partial differential equations[J].Acta Physica Sinica(物理学报),2004,53(9):2828-2830(in Chinese).
[10] Liu Shikuo,Fu Zuntao,Liu Shida,et al.A simple fast method in finding particular solutions of some nonlinear PDE[J].Applied Mathematics and Mechanics,2001,22(3):326-331.
[11] Benjamin T B,Bona J L,Mahony J J.Model equations for long waves in nonlinear dispersive systems[J].Philosophical Transactions for the Royal Society of London:Series A,1972,272:47-78.
[12] Vakhnenko V O,Parkes E J.The two loop soliton solution of the Vakhnenko equation[J].Nonlinearity,1998,11(6):1457-1464.
[13] Tso Taicheng.Existence of solutions of the modified Benjamin-Bone-Mahony equation[J].Chinese Journal of Mathematics,1996,24(4):327-336.
[14] Vakhnenko V O,Parkes E J.The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method[J].Chaos,Soliton and Fractals,2002,13(9):1819-1836.
[15] Yusufoglu E,Bekir A.The tanh and the sine-cosine methods for exact solutions of the MBBM and the Vakhnenko equations[J].Chaos,Soliton and Fractals,2008,38(4):1126-1133.
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