New multi-order envelope periodic solutions to cubic nonlinear Schr dinger equation

Ya-feng XIAO; Hai-li XUE; Hong-qing ZHANG

doi:10.3969/j.issn.1007-5461. 2012.03.003

[1] Miura M R. Bcklund Transformation ［M］. Berlin: Springer-Verlag, 1978.

[3] Hirota R. Exact solution of the Korteweg-de Vries for multiple collisions of solutions ［J］. Phys. Rev. Lett., 1971, 27: 1192-1194.

[4] Wang Mingliang. Solitary wave solutions for variant Boussinesq equations ［J］. Phys. Lett. A, 1996, 199: 169-172.

[5] Wang Mingliang, Zhou Yubin, Li Zhibin. Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics ［J］. Phys. Lett. A, 1996, 216: 67-75.

[6] Weiss J, Tabor M, Carnevale G. The Painlevé property for partial differential equations ［J］. J. Math. Phys., 1983, 24: 552-564.

[8] Nayfeh A H. Perturbation Methods ［M］. New York: John Wiley and Sons Inc., 1973.

[9] Liu Shikuo, Fu Zuntao, Liu Shida, et al. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations ［J］. Phys. Lett. A, 2001, 289: 69-74.

[10] Fu Zuntao, Liu Shikuo, Liu Shida, et al. The JEFE method and periodic solutions of two kinds of nonlinear wave equations ［J］. Commu. Nonlinear. Sci. Simul., 2003, 8: 67-75.

[12] Yan Zhenya. The extended Jacobian elliptic functions expansion method and its application in the generalized Hirota-Satsuma coupled KdV systems ［J］. Chaos, Solitons and Fractals, 2003, 15(3): 575-583.

[17] Liu Shikuo, Fu Zuntao, Liu Shida, et al. Lamé equation and multi-order exact solutions to nonlinear evolution equations ［J］. Chaos, Soliton and Fractals, 2004, 19: 795-801.

[20] Fu Zuntao, Yuan Naiming, et al. Multi-order exact solutions to the Drinfel’d-Sokolov-Wilson equations ［J］. Phys. Lett. A, 2009, 373: 3710-3714.

[21] Fu Zuntao, Yuan Naiming, et al. New Lamé equation and its application to nonlinear equations ［J］. Phys. Lett. A, 2009, 374: 214-217.

[22] Wang Zhuxi, Guo Dunren. Special Functions ［M］. Singapore: World Scientific Press, 1989.

[23] Fan Engui. Extended tanh-function method and its application to nonlinear equation ［J］. Phys. Lett. A, 2000, 277: 212-218.

[24] Kudryashov N A. Exact solutions of the generalized Kuramoto-Sivashinsky equation ［J］. Phys. Lett. A, 1990, 147: 287-291.

[25] Yan Chuntao. A simple transformation for nonlinear waves ［J］. Phys. Lett. A, 1996, 224: 77-84.