Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys.83, 247–305 (2011).

[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106, 213903 (2011).

[CrossRef]
[PubMed]

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A84, 023842 (2011).

[CrossRef]

M. Rietmann, R. Carretero-Gonzalez, and R. Chacon, “Controlling directed transport of matter wave solitons using the ratchet effect,” Phys. Rev. A83, 053617 (2011).

[CrossRef]

P. Papagiannis, Y. Kominis, and K. Hizanidis, “Power- and momentum-dependent soliton dynamics in lattices with longitudinal modulation,” Phys. Rev. A84, 013820 (2011).

[CrossRef]

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).

[CrossRef]
[PubMed]

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E82, 056606 (2010).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A81, 013624 (2010).

[CrossRef]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).

[CrossRef]

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev.3, 243–261 (2009).

[CrossRef]

K. Shandarova, C. E. Ruter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102, 123905 (2009).

[CrossRef]
[PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express16, 10309–10314 (2008).

[CrossRef]
[PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008).

[CrossRef]

D. Polleti, T. J. Alexander, E. A. Ostrovskaya, B. Li, and Y. S. Kivshar, “Dynamics of matter-wave solitons in a ratchet potential,” Phys. Rev. Lett.101, 150403 (2008).

[CrossRef]

F. Kh. Abdullaev, A. Gammal, H. L. F. da Luz, and L. Tomio, “Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice,” Phys. Rev. A76, 043611 (2007).

[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).

[CrossRef]
[PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett.32, 979–981 (2007).

[CrossRef]
[PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99, 213901 (2007).

[CrossRef]

Y. V. Kartashov and V. A. Vysloukh, “Anderson localization of solitons in optical lattices with random frequency modulation,” Phys. Rev. E72, 026606 (2005).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. A72, 046610 (2005).

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, “Dynamics of matter solitons in weakly modulated optical lattices,” Phys. Rev. A70, 043604 (2004).

[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424, 817–823 (2003).

[CrossRef]
[PubMed]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).

[CrossRef]
[PubMed]

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).

[CrossRef]
[PubMed]

A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose-Einstein condensates,” Phys. Rev. Lett.86, 2353–2356 (2001).

[CrossRef]
[PubMed]

F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose–Einstein condensates,” Phys. Rev. A64, 436061–4360610 (2001).

[CrossRef]

S. Flach, O. Yevtushenko, and Y. Zolotaryuk, “Directed current due to broken time-space symmetry,” Phys. Rev. Lett.84, 2358–2361 (2000).

[CrossRef]
[PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83, 4752–4755 (1999).

[CrossRef]

R. Scharf and A. R. Bishop, “Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials,” Phys. Rev. E47, 1375–1383 (1993).

[CrossRef]

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys.61, 763–915 (1989).

[CrossRef]

B. A. Malomed, “Evolution of nonsoliton and ’quasi-classical’ wavetrains in nonlinear Schrödinger and Korteweg–De Vries equations with dissipative perturbations,” Physica D29, 155–172 (1987).

[CrossRef]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A4, 651–654 (1987).

[CrossRef]

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).

[CrossRef]
[PubMed]

D. J. Kaup and A. C. Newell, “Solitons as particles, oscillators, and in slowly changing media: a singular perturbation theory,” Proc. R. Soc. London, Ser. A361, 413–446 (1978).

[CrossRef]

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E82, 056606 (2010).

[CrossRef]

F. Kh. Abdullaev, A. Gammal, H. L. F. da Luz, and L. Tomio, “Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice,” Phys. Rev. A76, 043611 (2007).

[CrossRef]

F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose–Einstein condensates,” Phys. Rev. A64, 436061–4360610 (2001).

[CrossRef]

D. Polleti, T. J. Alexander, E. A. Ostrovskaya, B. Li, and Y. S. Kivshar, “Dynamics of matter-wave solitons in a ratchet potential,” Phys. Rev. Lett.101, 150403 (2008).

[CrossRef]

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).

[CrossRef]
[PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008).

[CrossRef]

F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose–Einstein condensates,” Phys. Rev. A64, 436061–4360610 (2001).

[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).

[CrossRef]
[PubMed]

R. Scharf and A. R. Bishop, “Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials,” Phys. Rev. E47, 1375–1383 (1993).

[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83, 4752–4755 (1999).

[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, “Dynamics of matter solitons in weakly modulated optical lattices,” Phys. Rev. A70, 043604 (2004).

[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99, 213901 (2007).

[CrossRef]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).

[CrossRef]
[PubMed]

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).

[CrossRef]
[PubMed]

M. Rietmann, R. Carretero-Gonzalez, and R. Chacon, “Controlling directed transport of matter wave solitons using the ratchet effect,” Phys. Rev. A83, 053617 (2011).

[CrossRef]

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).

[CrossRef]
[PubMed]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).

[CrossRef]
[PubMed]

M. Rietmann, R. Carretero-Gonzalez, and R. Chacon, “Controlling directed transport of matter wave solitons using the ratchet effect,” Phys. Rev. A83, 053617 (2011).

[CrossRef]

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A84, 023842 (2011).

[CrossRef]

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).

[CrossRef]
[PubMed]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).

[CrossRef]

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A84, 023842 (2011).

[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106, 213903 (2011).

[CrossRef]
[PubMed]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics4, 103–106 (2010).

[CrossRef]

K. Shandarova, C. E. Ruter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102, 123905 (2009).

[CrossRef]
[PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express16, 10309–10314 (2008).

[CrossRef]
[PubMed]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008).

[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett.32, 979–981 (2007).

[CrossRef]
[PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99, 213901 (2007).

[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424, 817–823 (2003).

[CrossRef]
[PubMed]

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).

[CrossRef]
[PubMed]

F. Kh. Abdullaev, A. Gammal, H. L. F. da Luz, and L. Tomio, “Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice,” Phys. Rev. A76, 043611 (2007).

[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83, 4752–4755 (1999).

[CrossRef]

F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose–Einstein condensates,” Phys. Rev. A64, 436061–4360610 (2001).

[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99, 213901 (2007).

[CrossRef]

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).

[CrossRef]
[PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83, 4752–4755 (1999).

[CrossRef]

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A84, 023842 (2011).

[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature446, 52–55 (2007).

[CrossRef]
[PubMed]

S. Flach, O. Yevtushenko, and Y. Zolotaryuk, “Directed current due to broken time-space symmetry,” Phys. Rev. Lett.84, 2358–2361 (2000).

[CrossRef]
[PubMed]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).

[CrossRef]
[PubMed]

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).

[CrossRef]
[PubMed]

F. Kh. Abdullaev, A. Gammal, H. L. F. da Luz, and L. Tomio, “Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice,” Phys. Rev. A76, 043611 (2007).

[CrossRef]

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. (in press), doi: .

[CrossRef]

P. Papagiannis, Y. Kominis, and K. Hizanidis, “Power- and momentum-dependent soliton dynamics in lattices with longitudinal modulation,” Phys. Rev. A84, 013820 (2011).

[CrossRef]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).

[CrossRef]
[PubMed]

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).

[CrossRef]
[PubMed]

I. Kaminer, M. Segev, and D. N. Christodoulides, “Self-accelerating self-trapped optical beams,” Phys. Rev. Lett.106, 213903 (2011).

[CrossRef]
[PubMed]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys.83, 247–305 (2011).

[CrossRef]

Y. V. Kartashov and V. A. Vysloukh, “Anderson localization of solitons in optical lattices with random frequency modulation,” Phys. Rev. E72, 026606 (2005).

[CrossRef]

D. J. Kaup and A. C. Newell, “Solitons as particles, oscillators, and in slowly changing media: a singular perturbation theory,” Proc. R. Soc. London, Ser. A361, 413–446 (1978).

[CrossRef]

K. Shandarova, C. E. Ruter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102, 123905 (2009).

[CrossRef]
[PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express16, 10309–10314 (2008).

[CrossRef]
[PubMed]

D. Polleti, T. J. Alexander, E. A. Ostrovskaya, B. Li, and Y. S. Kivshar, “Dynamics of matter-wave solitons in a ratchet potential,” Phys. Rev. Lett.101, 150403 (2008).

[CrossRef]

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys.61, 763–915 (1989).

[CrossRef]

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. (in press), doi: .

[CrossRef]

P. Papagiannis, Y. Kominis, and K. Hizanidis, “Power- and momentum-dependent soliton dynamics in lattices with longitudinal modulation,” Phys. Rev. A84, 013820 (2011).

[CrossRef]

F. Kh. Abdullaev, V. V. Konotop, M. Salerno, and A. V. Yulin, “Dissipative periodic waves, solitons and breathers of the nonlinear Schrödinger equation with complex potentials,” Phys. Rev. E82, 056606 (2010).

[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, “Dynamics of matter solitons in weakly modulated optical lattices,” Phys. Rev. A70, 043604 (2004).

[CrossRef]

F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays of Bose–Einstein condensates,” Phys. Rev. A64, 436061–4360610 (2001).

[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, “Dynamics of matter solitons in weakly modulated optical lattices,” Phys. Rev. A70, 043604 (2004).

[CrossRef]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1–126 (2008).

[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature424, 817–823 (2003).

[CrossRef]
[PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83, 4752–4755 (1999).

[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett.23, 1701–1703 (1998).

[CrossRef]

D. Polleti, T. J. Alexander, E. A. Ostrovskaya, B. Li, and Y. S. Kivshar, “Dynamics of matter-wave solitons in a ratchet potential,” Phys. Rev. Lett.101, 150403 (2008).

[CrossRef]

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev.3, 243–261 (2009).

[CrossRef]

I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, “Light propagation and localization in modulated photonic lattices and waveguides,” Phys. Rep. (in press), doi: .

[CrossRef]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).

[CrossRef]
[PubMed]

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A84, 023842 (2011).

[CrossRef]

K. Shandarova, C. E. Ruter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102, 123905 (2009).

[CrossRef]
[PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express16, 10309–10314 (2008).

[CrossRef]
[PubMed]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys.83, 247–305 (2011).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A81, 013624 (2010).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. A72, 046610 (2005).

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys.61, 763–915 (1989).

[CrossRef]

B. A. Malomed, “Evolution of nonsoliton and ’quasi-classical’ wavetrains in nonlinear Schrödinger and Korteweg–De Vries equations with dissipative perturbations,” Physica D29, 155–172 (1987).

[CrossRef]

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58, 1499–1501 (1987).

[CrossRef]
[PubMed]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, “Josephson junction arrays with Bose-Einstein condensates,” Science293, 843–846 (2001).

[CrossRef]
[PubMed]

S. Burger, F. S. Cataliotti, C. Fort, F. Minardi, M. Inguscio, M. L. Chiofalo, and M. P. Tosi, “Superfluid and dissipative dynamics of a Bose–Einstein condensate in a periodic optical potential,” Phys. Rev. Lett.86, 4447–4450 (2001).

[CrossRef]
[PubMed]

G. Assanto, L. A. Cisneros, A. A. Minzoni, B. D. Skuse, N. F. Smyth, and A. L Worthy, “Soliton steering by longitudinal modulation of the nonlinearity in waveguide arrays,” Phys. Rev. Lett.104, 053903 (2010).

[CrossRef]
[PubMed]

R. El-Ganainy, K. G. Makris, M. A. Miri, D. N. Christodoulides, and Z. Chen, “Discrete beam acceleration in uniform waveguide arrays,” Phys. Rev. A84, 023842 (2011).

[CrossRef]

D. J. Kaup and A. C. Newell, “Solitons as particles, oscillators, and in slowly changing media: a singular perturbation theory,” Proc. R. Soc. London, Ser. A361, 413–446 (1978).

[CrossRef]

D. Polleti, T. J. Alexander, E. A. Ostrovskaya, B. Li, and Y. S. Kivshar, “Dynamics of matter-wave solitons in a ratchet potential,” Phys. Rev. Lett.101, 150403 (2008).

[CrossRef]

P. Papagiannis, Y. Kominis, and K. Hizanidis, “Power- and momentum-dependent soliton dynamics in lattices with longitudinal modulation,” Phys. Rev. A84, 013820 (2011).

[CrossRef]

K. Shandarova, C. E. Ruter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett.102, 123905 (2009).

[CrossRef]
[PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express16, 10309–10314 (2008).

[CrossRef]
[PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett.83, 4752–4755 (1999).

[CrossRef]

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