Zhang, Fei; Pérez-García, Víctor M.; Vázquez, Luis Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme. (English) Zbl 0832.65136 Appl. Math. Comput. 71, No. 2-3, 165-177 (1995). A new numerical scheme, conserving the energy and charge, for nonlinear Schrödinger type equations is presented. Reviewer: S.K.Rangarajan (Madras) Cited in 3 ReviewsCited in 142 Documents MSC: 65Z05 Applications to the sciences 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35Q55 NLS equations (nonlinear Schrödinger equations) 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics Keywords:nonlinear Schrödinger systems; conservative scheme PDFBibTeX XMLCite \textit{F. Zhang} et al., Appl. Math. Comput. 71, No. 2--3, 165--177 (1995; Zbl 0832.65136) Full Text: DOI References: [1] Hasegawa, A., Optical Solitons in Fibers (1989), Springer-Verlag: Springer-Verlag Berlin [2] Mollenauer, L. F.; Stolen, R. H.; Gordon, J. P., Phys. Rev. Lett., 45, 1095-1098 (1980) [3] Dodd, R. K.; Eibeck, J. C.; Gibbon, J. D.; Morris, H. C., Solitons and Nonlinear Wave Equation (1982), Academic Press · Zbl 0496.35001 [4] Davydov, A. S., Solitons in Molecular Systems (1985), Reidel: Reidel Dordrecht · Zbl 0597.35001 [5] Zakharov, V. E.; Shabat, A. B., Soviet Phys. JETP, 34, 62-69 (1972) [6] Sanz-Serna, J. M., SIAM J. Sci. Stat. Comput., 6, 923 (1985) [7] Herbst, B. M.; Ablowitz, M. J., Phys. Rev. Lett., 62, 2065-2068 (1989) [8] McLaughlin, D. W.; Schober, C., Physica D, 57, 447-465 (1992) [9] Jimenez, S.; Vázquez, L., Appl. Math. Comput., 35, 61-93 (1990) [10] Strauss, W. A., (de la Penha, G. M.; Madeiros, L. A., Contemporary Developments in Continuum Mechanics and Partial Differential Equations (1978), North-Holland: North-Holland New York) [11] Delfour, M.; Fortin, M.; Payre, G., J. Comput. Phys., 44, 277-288 (1981) [12] Taha, T. R.; Ablowitz, M., J. Comput. Phys., 55, 203-230 (1984) [13] Sanz-Serna, J. M., Math. Comp., 43, 21-32 (1984) [14] Herbst, B. M.; Morris, J. Ll.; Mitchell, A. R., J. Comput. Phys., 60, 282-305 (1985) [15] Guo, B. Y., J. Comput. Math., 4, 121 (1986) [16] Tourigny, Y.; Morris, J., J. Comput. Phys., 76, 103-130 (1988) [17] Sanz-Serna, J. M.; Verwer, J. G., IMA J. Numer. Anal., 6, 25-42 (1986) [18] Strauss, W. A.; Vazquez, L., J. Comput. Phys., 28, 271-278 (1978) [19] Ben-Yu, Guo; Pascual, P. J.; Rodriguez, M. J.; Vazquez, L., Appl. Math. Comput., 18, 1-14 (1986) [20] Fei, Zhang; Vázquez, L., Appl. Math. Comput., 45, 17-30 (1991) [21] Cloot, A.; Herbst, B. M.; Weideman, J. A.C., J. Comput. Phys., 86, 127-146 (1990) [22] Miles, J. W., SIAM J. Appl. Math., 41, 227 (1981) [23] Kivshar, Yu. S.; Malomed, B. A., Rev. Mod. Phys., 61, 765-915 (1989) [24] Agrawall, G. P., Nonlinear Fiber Optics (1989), Academic Press: Academic Press New York [25] Suydam, B. R., IEEE J. Quant. Elect., 10/11, 837-843 (1974) [26] Lugiato, L. A.; Oldano, C.; Narducci, L. M., J. Opt. Soc. Am., B5, 879-888 (1988) [27] Peranich, L. S., J. Comput. Phys., 68, 501-505 (1987) [28] Menyuk, C. R., IEEE J. Quant. Elect., 25, 2674-2682 (1989) [29] Trillo, S.; Wabnitz, S.; Wright, E. M.; Stegeman, G. I., Opt. Lett., 13, 672-674 (1988) 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.