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The existence of standing wave for the discrete coupled nonlinear Schrödinger lattice. (English) Zbl 1236.35168

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.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
39A12 Discrete version of topics in analysis
81Q80 Special quantum systems, such as solvable systems
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[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)
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