In this section, we will review work on few-lattice-site systems of the so-called discrete self-trapping (DST) equations, where we will discuss the integrability of few-lattice-site DST systems, the present of chaos in nonintegrable ones, their applications as well as experimental observations of the systems.
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References
Eilbeck, J.C., Lomdahl, P.S., Scott, A.C.: Physica D 16, 318 (1985)
Eilbeck, J.C., Johansson, M.: The Discrete Nonlinear Schrödinger equation – 20 Years on. In: Localization and Energy Transfer in Nonlinear Systems, Vázquez, L., Mackay, R.S., Zorzano, M.P. (eds.), pp. 44–67. World Scientific, New Jersey (2003)
Scott, A.C.: Nonlinear Science: Emergence and Dynamics of Coherent Structures, 2nd edn. Oxford University Press, New York (2003)
Landau, L.D.: Phys. Zeit. Sowjetunion 3, 664 (1933)
Scott, A.C., Lomdahl, P.S., Eilbeck, J.C.: Chem. Phys. Letts. 113, 29–36 (1985)
MarÃin, J.L., Aubry, S.: Physica D 119, 163–174 (1998)
Buonsante, P., Kevrekidis, P.G., Penna, V., Vezzani, A.: Phys. Rev. E 75, 016212 (2007)
Arnold, V.I. (ed.): Dynamical Systems III. Springer, Berlin (1988)
Libermann, P., Marle, C.M.: Symplectic Geometry and Analytical Mechanics. Reidel, Dordrecht (1987)
Kenkre, V.M., Campbell, D.K.: Phys. Rev. B 34, 4959 (1986)
Jensen, J.H., Christiansen, P.L., Elgin, J.N., Gibbon, J.D., Skovgaard, O.: Phys. Lett. A 110, 429 (1985)
Cruzeiro-Hansson, L., Christiansen, P.L., Elgin, J.N.: Phys. Rev. B 37, 7896 (1988)
Khomeriki, R., Leon, J., Ruffo, S.: Phys. Re. Lett. 97, 143902 (2006)
Khomeriki, R., Leon, J., Ruffo, S., Wimberger, S.: Theor. Math. Phys. 152, 1122 (2007)
Scott, A.C., Christiansen, P.L.: Phys. Scri. 42, 257–262 (1990)
Jørgensen, M.F., Christiansen, P.L., Abou-Hayt, I.: Physica D 68, 180–184 (1993)
Jørgensen, M.J., Christiansen, P.L., Chaos, Solitons & Fractals 4, 217–225 (1994)
Jørgensen, M.F., Christiansen, P.L.: J. Phys. A: Math. Gen. 31, 969–976 (1998)
Henning, D.: J. Phys. A: Math. Gen. 25, 1247 (1992)
Hennig, D.: Physica D 64, 121 (1993)
Christiansen, P.L., Jørgensen, M.F., Kuznetsov, V.B.: Lett. Math. Phys. 29, 165-73 (1993)
Defilippo, S., Girard, M.F., Salerno, M.: Physica D 26, 411 (1987)
Molina, M.I., Tsironis, G.P.: Phys. Rev. A 46, 1124–1127 (1992)
Hennig, D., Gabriel, H., Jørgensen, M.F., Christiansen, P.L., Clausen, C.B.: Phys. Rev. E 51, 2870 (1995)
Hennig, D., Gabriel, H.: J. Phys. A: Math. Gen. 28, 3749 (1995)
Feddersen, H., Christiansen, P.L., Salerno, M.: Phys. Scr. 43, 353 (1991)
Bang, O., Christiansen, P.L., Clausen, C.B.: Phys. Rev. E 56, 7257–7266 (1997)
Hennig, D.: Phys. Scr. 46, 14–19 (1992)
Christodoulides, D.N., Lederer, F., Silberberg, Y.: Nature 424, 817 (2003)
Slusher, R.E., Eggleton, B.J. (eds.): Nonlinear Photonic Crystals. Springer, Berlin Heidelberg New York (2004)
Pitaevskii, L.P., Stringari, S.: Bose-Einstein Condensation. Oxford University Press, Oxford (2003)
Kevrekidis, P.G., Frantzeskakis, D.J., Carretero-González, R., (eds.): Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment. Springer, Berlin Heidelberg New York (2008)
Smerzi, A., Fantoni, S., Giovanazzi, S., Shenoy, S.R.: Phys. Rev. Lett. 79, 4950 (1997)
Pelinovsky, D.E.: Asymptotic reductions of the Gross-Pitaevskii equation. In: [38] pp. 377–398. 178
Theocharis, G., Kevrekidis, P.G., Frantzeskakis, D.J., Schmelcher, P.: Phys. Rev. E 74, 056608 (2006)
Raghavan, S., Smerzi, A., Fantoni, S., Shenoy, S.R.: Phys. Rev. A 59, 620 (1999)
Albiez, M., Gati, R., Fölling, J., Hunsmann, S., Cristiani, M., Oberthaler, M.K.: Phys. Rev. Lett. 95, 010402 (2005)
Gati, R., Albiez, M., Fölling, J., Hemmerling, B., Oberthaler, M.K.: Appl. Phys. B 82, 207 (2006)
Buonsante, P., Franzosi, R., Penna, V.: Phys. Rev Lett. 90, 050404 (2003)
Pando, C.L., Doedel, E.J.: Phys. Rev. E 69, 042403 (2004)
Pando, C.L., Doedel, E.J.: Phys. Rev. E 71, 056201 (2007)
Cataliotti, F.S., Burger, S., Fort, C., Maddaloni, P., Minardi, F., Trombettoni, A., Smerzi, A., Inguscio, M.: Science 293, 843 (2001)
Jensen, S.M., IEEE J. Quantum Electron. QE-18, 1580 (1982)
Kevrekidis, P.G., Chen, Z., Malomed, B.A., Frantzeskakis, D.J., Weinstein, M.I.: Phys. Lett. A 340, 275 (2005)
Finlayson, N., Stegeman, G.I.: Appl. Phys. Lett. 56, 2276 (1990)
Molina, M.I., Deering, W.D., Tsironis, G.P.: Physica D 66, 135–142 (1993)
Tsironis, G.P., Deering, W.D., Molina, M.I.: Physica D 68, 135–137 (1993)
Kapitula, T., Kevrekidis, P.G., Chen, Z.: SIAM J. Appl. Dyn. Syst. 5, 598 (2006)
Khomeriki, R., Leon, J.: Phys. Rev. Lett. 94, 243902 (2005)
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Susanto, H. (2009). Few-Lattice-Site Systems of Discrete Self-Trapping Equations. In: The Discrete Nonlinear Schrödinger Equation. Springer Tracts in Modern Physics, vol 232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89199-4_13
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