Liu, Ling; Yan, Weiping; Zhao, Xin The existence of standing wave for the discrete coupled nonlinear Schrödinger lattice. (English) Zbl 1236.35168 Phys. Lett., A 374, No. 15-16, 1690-1693 (2010). Summary: In this Letter, we consider the existence of standing wave for the discrete coupled nonlinear Schrödinger lattice. Our method is based on Nehari’s manifold approach. Cited in 2 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 39A12 Discrete version of topics in analysis 81Q80 Special quantum systems, such as solvable systems Keywords:nonlinear Schrödinger lattice; standing wave; Nehari’s manifold approach PDFBibTeX XMLCite \textit{L. Liu} et al., Phys. Lett., A 374, No. 15--16, 1690--1693 (2010; Zbl 1236.35168) Full Text: DOI References: [1] Pitaevskii, L.; Stingari, S., Bose-Einstein Condensation (2003), Oxford University Press: Oxford University Press Oxford [2] Ambrosetti, N.; Colorado, E., J. London Math. Soc., 75, 67 (2007) [3] Belmonte-Beitia, V. M.; Pérez-García, J.; Torres, P. J., J. Nonlinear Science, 19, 1437 (2009) [4] Hioe, F. T., Phys. Rev. Lett., 82, 1152 (1999) [5] Kanna, T.; Lakshmanan, M., Phys. Rev. Lett., 86, 5043 (2001) [6] Aubry, S., Physica D, 103, 201 (1997) [7] Hennig, D.; Tsironis, G. P., Phys. Rep., 307, 333 (1999) [8] Rothos, V. M.; Bountis, T. C., Physica D, 113, 326 (1998) [9] Aubry, S., Physica D, 71, 196 (1994) [10] Johansson, M.; Aubry, S., Nonlinearity, 10, 1151 (1997) [11] Mackay, R. S.; Aubry, S., Nonlinearity, 7, 1623 (1994) [12] Karachalios, N. I.; Yannacopoulos, A. N., J. Diff. Eqns., 217, 88 (2005) [13] Pankov, A.; Rothos, V., Proc. Roy. Soc. A, 464, 3219 (2008) [14] Zhang, G. P., J. Math. Phys., 50, 1, 1 (2009) [15] Mitchell, M.; Chen, Z.; Shin, M.; Segev, M., Phys. Rev. Lett., 77, 490 (1996) [16] Mitchell, M.; Segev, M., Nature, 387, 880 (1997) 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.