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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 979252, 7 pages
Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive Term
1Department of Mathematics, Heze University, Heze 274000, China
2College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China
Received 12 July 2013; Accepted 10 September 2013
Academic Editor: Yong Hong Wu
Copyright © 2013 Rui Cao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- W.-X. Ma and M. Chen, “Direct search for exact solutions to the nonlinear Schrödinger equation,” Applied Mathematics and Computation, vol. 215, no. 8, pp. 2835–2842, 2009.
- M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, vol. 4, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 1981.
- A. Hasegawa and Y. Kodama, Solitons in Optical Communications, Oxford University Press, New York, NY, USA, 1995.
- L. X. Li and M. L. Wang, “The -expansion method and travelling wave solutions for a higher-order nonlinear Schrödinger equation,” Applied Mathematics and Computation, vol. 208, no. 2, pp. 440–445, 2009.
- W.-X. Ma and J.-H. Lee, “A transformed rational function method and exact solutions to the dimensional Jimbo-Miwa equation,” Chaos, Solitons & Fractals, vol. 42, no. 3, pp. 1356–1363, 2009.
- F. X. Wu and Z. D. Dai, “New bright and dark solitons for quintic nonlinear derivative Schrödinger equation,” Applied Mathematics and Computation, vol. 218, no. 18, pp. 9305–9309, 2012.
- W. X. Ma, “Bilinear equations, Bell polynomials and linear superposition princ,” Journal of Physics, vol. 411, Article ID iple012021, 2013.
- Y. Liu, “Exact solutions to nonlinear Schrödinger equation with variable coefficients,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5866–5869, 2011.
- N. Taghizadeh and M. Mirzazadeh, “The simplest equation method to study perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 4, pp. 1493–1499, 2012.
- N. A. Kudryashov, “On types of nonlinear nonintegrable equations with exact solutions,” Physics Letters A, vol. 155, no. 4-5, pp. 269–275, 1991.
- R. Hirota, The Direct Method in Soliton Theory, vol. 155, Cambridge University Press, Cambridge, UK, 2004.
- A. M. Wazwaz, “On multiple soliton solutions for coupled kdv-mkdv equation,” Nonlinear Science Letters A, vol. 1, no. 3, pp. 289–296, 2010.
- R. Hirota, “Direct method of finding exact solutions of nonlinear evolution equations,” in Bäcklund transformations, R. Bullough and P. Caudrey, Eds., Springer, Berlin, Germany, 1980.
- A.-M. Wazwaz, “A sine-cosine method for handling nonlinear wave equations,” Mathematical and Computer Modelling, vol. 40, no. 5-6, pp. 499–508, 2004.
- A.-M. Wazwaz, “The tanh method for traveling wave solutions of nonlinear equations,” Applied Mathematics and Computation, vol. 154, no. 3, pp. 713–723, 2004.
- E. G. Fan, “Extended tanh-function method and its applications to nonlinear equations,” Physics Letters A, vol. 277, no. 4-5, pp. 212–218, 2000.
- J.-H. He and X.-H. Wu, “Exp-function method for nonlinear wave equations,” Chaos, Solitons & Fractals, vol. 30, no. 3, pp. 700–708, 2006.
- W.-X. Ma and Z. Zhu, “Solving the -dimensional generalized KP and BKP equations by the multiple exp-function algorithm,” Applied Mathematics and Computation, vol. 218, no. 24, pp. 11871–11879, 2012.
- E. G. Fan and J. Zhang, “Applications of the Jacobi elliptic function method to special-type nonlinear equations,” Physics Letters A, vol. 305, no. 6, pp. 383–392, 2002.
- Z. S. Feng, “The first-integral method to study the Burgers-Korteweg-de Vries equation,” Journal of Physics A, vol. 35, no. 2, pp. 343–349, 2002.
- W.-X. Ma, “Comment on the dimensional Kadomtsev-Petviashvili equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 7, pp. 2663–2666, 2011.
- F. D. Xie, Y. Zhang, and Z. S. Lü, “Symbolic computation in non-linear evolution equation: application to -dimensional Kadomtsev-Petviashvili equation,” Chaos, Solitons and Fractals, vol. 24, no. 1, pp. 257–263, 2005.
- C. P. Liu, “Exact solutions for the higher-order nonlinear Schördinger equation in nonlinear optical fibres,” Chaos, Solitons and Fractals, vol. 23, no. 3, pp. 949–955, 2005.
- S. Y. Lai, X. M. Lv, and M. Y. Shuai, “The Jacobi elliptic function solutions to a generalized Benjamin-Bona-Mahony equation,” Mathematical and Computer Modelling, vol. 49, no. 1-2, pp. 369–378, 2009.