Zhang, Zai-Yun; Liu, Zhen-Hai; Miao, Xiu-Jin; Chen, Yue-Zhong New exact solutions to the perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity. (English) Zbl 1195.35283 Appl. Math. Comput. 216, No. 10, 3064-3072 (2010). Summary: By using the modified mapping method and the extended mapping method, we derive some new exact solutions of the perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity, which are the linear combination of two different Jacobi elliptic functions and we also consider the solutions in the limit cases. Cited in 1 ReviewCited in 24 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 35A24 Methods of ordinary differential equations applied to PDEs Keywords:perturbed nonlinear Schrödinger’s equation; exact solutions; modified mapping method; extended mapping method; Kerr law nonlinearity PDF BibTeX XML Cite \textit{Z.-Y. Zhang} et al., Appl. Math. Comput. 216, No. 10, 3064--3072 (2010; Zbl 1195.35283) Full Text: DOI OpenURL References: [1] Matveev, V.B.; Salle, M.A., Darboux transformations and solitons, (1991), Springer Berlin · Zbl 0744.35045 [2] Lamb, G.L., Elements of soliton theory, (1980), Wliley NewYork · Zbl 0445.35001 [3] Li, B.; Chen, Y.; Zhang, H.Q., Auto-backlund transformation and exact solutions for the compound KDV-type and compound KDV-Burgers-type equations with nonlinear terms of any order, Phys. lett. A, 305, 6, 377-382, (2002) · Zbl 1005.35079 [4] Fan, En-Gui, A series of new exact solutions for a complex coupled KDV system, Chaos solitons fract., 19, 3, 515-525, (2004) · Zbl 1068.35130 [5] Malfliet, W., The tanh method: a tool for solving certain classes of nonlinear evolution and wave equations, J. comput. appl. math., 164, 1, 529-541, (2004) · Zbl 1038.65102 [6] Soliman, A.A., The modified extended tanh-function method for solving Burgers-type equations, Physica A, 169, 46, 1254-1258, (1997) [7] Fan, En-Gui; Zhang, H.Q., The solitary wave solutions for a class of nonlinear wave equations, Acta phys. sin., 361, 2, 394-404, (2006) [8] Lu, Da-Zhao, Abundant Jacobi elliptic function solutions of nonlinear evolution equations, Acta phys. sin., 54, 10, 4501-4505, (2005) · Zbl 1202.33029 [9] Liu, Shi-Kuo, Jacobi elliptic function expansion solution to the variable coefficient nonlinear equations, Acta phys. sin., 51, 9, 1925-1926, (2002) · Zbl 1202.35056 [10] Fan, En-Gui; Hon Benny, Y.C., Double periodic solitons with Jacobi elliptic functions for two generalized hirota – satsumn coupled KDV systems, Phys. lett. A, 292, 6, 335-337, (2002) · Zbl 1098.35559 [11] Peng, Yan-Ze, Exact periodic wave solutions to a new Hamitonian amplitude equation, J. phys. soc. jpn., 72, 6, 1356-1359, (2003) · Zbl 1054.35004 [12] Gong, Lun-Xun, Some new exact solutions of the Jacobi elliptic functions of NLS equation, Acta phys. sin., 55, 9, 4414-4419, (2006) · Zbl 1202.35222 [13] M.J. Ablowitz, H. Segur, Solitons and Inverse Scattering Transform, SIAM, Philadelphia, PA, USA, 1981. · Zbl 0472.35002 [14] Wabnitz, S.; Kodama, Y.; Aceves, A.B., Control of optical soliton interactions, Opt. fiber technol., 1, 187-217, (1995) [15] Biswas, A.; Konar, S., Introduction to non-Kerr law optical solitons, (2007), CRC Press, USA Boca Raton, FL · Zbl 1156.78001 [16] Kohl, R.; Biswas, A.; Milovic, D.; Zerradc, E., Optical soliton perturbation in a non-kerrlaw media, Optics laser technol., 40, 647-C662, (2008) [17] P.D. Green, A. Biswas, Bright and dark optical solitons with time-dependent coefficients in a non-Kerr law media, Commun. Nonlinear Sci. Numer. Sim., in press, doi:10.1016/j.cnsns.2010.01.018. · Zbl 1222.78040 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.