[1] Russell J S 1844 Fourteenth Meeting of the British
Association for the Advancement of Science 26 September--2 October 1844
(London: John Murray) p 311

[2] Ablowitz M J and Segur H 1981 Solitons and the
Inverse Scattering Transformations (Philadelphia: SIAM)

[3] Gu C H et al 1990 Theory and Application of Solitons
(Hangzhou: Zhejiang Science and Technology Press) (in Chinese)

[4] Fermi A, Pasta J and Ulam S 1940 Los Alamos Sci.
Lab. Report
Fermi A, Pasta J and Ulam S 1955 Los
Alamos National Laboratory

[5] Perring J K, Skyrime and T H R 1962 Nucl. Phys.
31 550

[6] Zabusky N J and Kruskal M D 1965 Phys. Rev. Lett.
15 240

[7] Guo B Y 1990 Theory and Application of Solitons (in
Chinese) (Hangzhou: Zhejiang Science and Technology Press)

[8] Aoyagi A 1989 J. Comput. Phys. 83 447

[9] Herman R L 1993 J. Comput. Phys. 104 50

[10] Olver P J 1991 Applications of Lie Groups to
Differential Equations 2nd edn (New York: Springer)

[11] Ran Z 2005 Chin. Q. Mech. 26 650 (in Chinese)

[12] Ran Z 2007 SIAM J. Numer. Anal. 46 325

[13] Ran Z 2007 Chin. Phys. Lett. 24 3332

Ran Z 2008 Chin. Phys. Lett. 25 3867

[14] Chen J B et al 2002 SIAM J. Numer. Anal. 39
2164

[15] Chen J B et al 2008 Chin. Phys. Lett. 4 1168

[16] Ran Z 2008 Lie Symmetries Preservation and the
Soliton Calculation (Report of SIAM).