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. A 84, 023842 (2011).

[CrossRef]

M. Rietmann, R. Carretero-Gonzalez, and R. Chacon, “Controlling directed transport of matter wave solitons using the ratchet effect,” Phys. Rev. A 83, 053617 (2011).

[CrossRef]

P. Papagiannis, Y. Kominis, and K. Hizanidis, “Power- and momentum-dependent soliton dynamics in lattices with longitudinal modulation,” Phys. Rev. A 84, 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. E 82, 056606 (2010).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81, 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. Photonics 4, 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. Express 16, 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. A 76, 043611 (2007).

[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 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. E 72, 026606 (2005).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. A 72, 046610 (2005).

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, “Dynamics of matter solitons in weakly modulated optical lattices,” Phys. Rev. A 70, 043604 (2004).

[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 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,” Science 293, 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. A 64, 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. E 47, 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 D 29, 155–172 (1987).

[CrossRef]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 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. A 361, 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. E 82, 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. A 76, 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. A 64, 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. A 64, 436061–4360610 (2001).

[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 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. E 47, 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. A 70, 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]

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,” Science 293, 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. A 83, 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,” Science 293, 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. A 83, 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. A 84, 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. Photonics 4, 103–106 (2010).

[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. A 84, 023842 (2011).

[CrossRef]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 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]

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]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16, 10309–10314 (2008).

[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]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 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. A 76, 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. A 64, 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. A 84, 023842 (2011).

[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 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,” Science 293, 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. A 76, 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. A 84, 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,” Science 293, 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. E 72, 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. A 361, 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. Express 16, 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. A 84, 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. E 82, 056606 (2010).

[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, “Dynamics of matter solitons in weakly modulated optical lattices,” Phys. Rev. A 70, 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. A 64, 436061–4360610 (2001).

[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, “Dynamics of matter solitons in weakly modulated optical lattices,” Phys. Rev. A 70, 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,” Nature 424, 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,” Science 293, 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. A 84, 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. Express 16, 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. A 81, 013624 (2010).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. A 72, 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 D 29, 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,” Science 293, 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. A 84, 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. A 361, 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. A 84, 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. Express 16, 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]

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]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).

[CrossRef]

M. Rietmann, R. Carretero-Gonzalez, and R. Chacon, “Controlling directed transport of matter wave solitons using the ratchet effect,” Phys. Rev. A 83, 053617 (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]

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81, 013624 (2010).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. A 72, 046610 (2005).

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. E 82, 056606 (2010).

[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. A 64, 436061–4360610 (2001).

[CrossRef]

R. Scharf and A. R. Bishop, “Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials,” Phys. Rev. E 47, 1375–1383 (1993).

[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).

[CrossRef]
[PubMed]

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

[CrossRef]
[PubMed]

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]

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]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16, 10309–10314 (2008).

[CrossRef]
[PubMed]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).

[CrossRef]
[PubMed]

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]

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,” Nature 424, 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]

A. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose-Einstein condensates,” Phys. Rev. Lett. 86, 2353–2356 (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,” Science 293, 843–846 (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]

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]

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. 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. A 76, 043611 (2007).

[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (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. Trombettoni and A. Smerzi, “Discrete solitons and breathers with dilute Bose-Einstein condensates,” Phys. Rev. Lett. 86, 2353–2356 (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,” Science 293, 843–846 (2001).

[CrossRef]
[PubMed]

Y. V. Kartashov and V. A. Vysloukh, “Anderson localization of solitons in optical lattices with random frequency modulation,” Phys. Rev. E 72, 026606 (2005).

[CrossRef]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).

[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]

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. 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. E 82, 056606 (2010).

[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]

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

[CrossRef]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).

[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).

[CrossRef]
[PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).

[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]

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, “Dynamics of matter solitons in weakly modulated optical lattices,” Phys. Rev. A 70, 043604 (2004).

[CrossRef]

M. Rietmann, R. Carretero-Gonzalez, and R. Chacon, “Controlling directed transport of matter wave solitons using the ratchet effect,” Phys. Rev. A 83, 053617 (2011).

[CrossRef]

P. Papagiannis, Y. Kominis, and K. Hizanidis, “Power- and momentum-dependent soliton dynamics in lattices with longitudinal modulation,” Phys. Rev. A 84, 013820 (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. A 84, 023842 (2011).

[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. A 76, 043611 (2007).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. A 72, 046610 (2005).

H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81, 013624 (2010).

[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. A 64, 436061–4360610 (2001).

[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. E 82, 056606 (2010).

[CrossRef]

R. Scharf and A. R. Bishop, “Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials,” Phys. Rev. E 47, 1375–1383 (1993).

[CrossRef]

Y. V. Kartashov and V. A. Vysloukh, “Anderson localization of solitons in optical lattices with random frequency modulation,” Phys. Rev. E 72, 026606 (2005).

[CrossRef]

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

[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]

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]

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]

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]

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

[CrossRef]

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

[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]

B. A. Malomed, “Evolution of nonsoliton and ’quasi-classical’ wavetrains in nonlinear Schrödinger and Korteweg–De Vries equations with dissipative perturbations,” Physica D 29, 155–172 (1987).

[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. A 361, 413–446 (1978).

[CrossRef]

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

[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (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,” Science 293, 843–846 (2001).

[CrossRef]
[PubMed]

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]

N. Akhmediev and A. Ankiewicz, eds., Dissipative Solitons, Lect. Notes Phys. (Springer, 2005), Vol. 661.

[CrossRef]