Li, Biao; Chen, Yong On exact solutions of the nonlinear Schrödinger equations in optical fiber. (English) Zbl 1049.35169 Chaos Solitons Fractals 21, No. 1, 241-247 (2004). Summary: With the help of symbolic computation, the projective Riccati equations method is extended to find some new exact solutions of the nonlinear Schrödinger model with varying dispersion, nonlinearity, and gain or absorption. As a result, four families of Soliton-like solutions in these models are obtained. Cited in 14 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 35Q51 Soliton equations 35Q60 PDEs in connection with optics and electromagnetic theory 78A60 Lasers, masers, optical bistability, nonlinear optics 35-04 Software, source code, etc. for problems pertaining to partial differential equations Software:Maple PDFBibTeX XMLCite \textit{B. Li} and \textit{Y. Chen}, Chaos Solitons Fractals 21, No. 1, 241--247 (2004; Zbl 1049.35169) Full Text: DOI References: [1] Gardner, C. S.; Greene, J. M.; Kruskal, M. D.; Miura, R. M., Phys. Rev. Lett., 19, 1095 (1967) [2] Iizuka, T.; Wadati, M.; Yajima, T., J. Phys. Soc. Jpn., 60, 2862 (1991) [3] Konno, K.; Wadati, M., Prog. Theor. Phys., 53, 1652 (1975) [4] Hirota, R., Phys. Rev. Lett., 27, 1192 (1971) [5] Malfliet, W.; Hereman, W., Phys. Scr., 54, 563 (1996) [6] Parkes, E. J.; Duffy, B. R., Phys. Lett. A, 229, 217 (1997) · Zbl 0972.35528 [7] Fan, E., Phys. Lett. A, 294, 26 (2002) [8] Elwakil, S. A.; El-labany, S. K.; Zahran, M. A.; Sabry, R., Phys. Lett. A, 299, 179 (2002) [9] Yan, Z. Y.; Zhang, H. Q., Phys. Lett. A, 285, 355 (2001) [10] Lü, Z. S.; Zhang, H. Q., Chaos, Solitons & Fractals, 17, 669 (2003) [11] Li, B.; Chen, Y.; Zhang, H. Q., Chaos, Solitons & Fractals, 15, 647 (2003) [12] Tian, B.; Gao, Y. T., Z. Natur. A, 57, 39 (2002) [13] Chen, Y.; Li, B.; Zhang, H. Q., Commun. Theor. Phys., 40, 137 (2003) [14] Conte, R.; Musette, M., J. Phys. A, 25, 5609 (1992) [15] Bountis, T. C.; Papageorgiou, V.; Winternitz, P., J. Math. Phys., 27, 1215 (1986) [16] Zhang, G. X.; Li, Z. B.; Duan, Y. S., Sci. Chin. Ser. A, 44, 396 (2001) [17] Yan, Z. Y., Chaos, Solitons & Fractals, 16, 759 (2003) [18] Chen, Y.; Li, B., Chaos, Solitons & Fractals, 19, 977 (2004) [19] Bordon, E. E.; Anderson, W. L., J. Lightwave Technol., 7, 353 (1989) [20] Kivshar, Yu. S.; Konotop, V. V., Sov. J. Quant. Electron., 19, 566 (1989) [21] Wen, S. C.; Xu, W. C.; Guo, Q.; Liu, S. H., Sci. Chin. Ser. A, 27, 949 (1997) [22] Ruan, H. Y.; Chen, Y. X., J. Phys. Soc. Jpn., 72, 1350 (2003) 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.