Explicit and exact solutions to the mBBM and Vakhnenko equations

Peng GUO; Lei ZHANG; Xiao-yun WANG; Xiao-wei SUN

[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.

[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.

[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.