[1] C. J.Pethick and H.Smith, Bose–Einstein Condensation in Dilute Gases, Cambridge University Press, Cambridge (2008).

[2] V. A. Brazhnyi, V. V. Konotop. Theory of nonlinear matter waves in optical lattices. Mod. Phys. Lett. B, 2004, 18(14): 627-651.

[3] O. Morsch, M. Oberthaler. Dynamics of Bose–Einstein condensates in optical lattices. Rev. Mod. Phys., 2006, 78(1): 179-215.

[4] M. Lewenstein, et al.. Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys., 2007, 56(2): 243-379.

[5] M.Lewenstein, A.Sanpera and V.Ahufinger, Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems, Oxford University Press, Oxford (2012).

[6] P. Windpassinger, K. Sengstock. Engineering novel optical lattices. Rep. Prog. Phys., 2013, 76(8): 086401.

[7] K. V. Krutitsky. Ultracold bosons with short-range interaction in regular optical lattices. Phys. Rep., 2016, 607: 1-101.

[8] M. Combescot, R. Combescot, F. Dubin. Bose–Einstein condensation and indirect excitons: a review. Rep. Prog. Phys., 2017, 80(6): 066501.

[9] C. Schneider, et al.. Exciton-polariton trapping and potential landscape engineering. Rep. Prog. Phys., 2016, 80(1): 016503.

[10] P. Pedri, L. Santos. Two-dimensional bright solitons in dipolar Bose–Einstein condensates. Phys. Rev. Lett., 2005, 95(20): 200404.

[11] J. H. V. Nguyen, et al.. Collisions of matter-wave solitons. Nat. Phys., 2014, 10(12): 918-922.

[12] E. A. Cerda-Méndez, et al.. Exciton-polariton gap solitons in two-dimensional lattices. Phys. Rev. Lett., 2013, 111(14): 146401.

[13] J. H. V. Nguyen, D. Luo, R. G. Hulet. Formation of matter-wave soliton trains by modulational instability. Science, 2017, 356(6336): 422-426.

[14] R. Dum, et al.. Creation of dark solitons and vortices in Bose–Einstein condensates. Phys. Rev. Lett., 1998, 80(14): 2972-2975.

[15] T. Busch, J. R. Anglin. Motion of dark solitons in trapped Bose–Einstein condensates. Phys. Rev. Lett., 2000, 84(11): 2298-2301.

[16] S. Stellmer, et al.. Collisions of dark solitons in elongated Bose–Einstein condensates. Phys. Rev. Lett., 2008, 101(12): 120406.

[17] A. Weller, et al.. Experimental observation of oscillating and interacting matter wave dark solitons. Phys. Rev. Lett., 2008, 101(13): 130401.

[18] C. Becker, et al.. Oscillations and interactions of dark and dark-bright solitons in Bose–Einstein condensates. Nat. Phys., 2008, 4(6): 496-501.

[19] I. Shomroni, et al.. Evidence for an oscillating soliton/vortex ring by density engineering of a Bose–Einstein condensate. Nat. Phys., 2009, 5(3): 193-197.

[20] D. J. Frantzeskakis. Dark solitons in atomic Bose–Einstein condensates: from theory to experiments. J. Phys. A, 2010, 43(21): 213001.

[21] P. G.Kevrekidis, D. J.Frantzeskakis and R.Carretero-González, The Defocusing Nonlinear Schrödinger Equation: From Dark Solitons to Vortices and Vortex Rings, SIAM, Philadelphia, Pennsylvania (2015).

[22] F. Tsitoura, et al.. Dark solitons near potential and nonlinearity steps. Phys. Rev. A, 2016, 94(6): 063612.

[23] M. Sciacca, C. F. Barenghi, N. G. Parker. Matter-wave dark solitons in boxlike traps. Phys. Rev. A, 2017, 95: 013628.

[24] L. M. Aycock, et al.. Brownian motion of solitons in a Bose–Einstein condensate. Proc. Natl. Acad. Sci. U.S.A., 2017, 114(10): 2503-2508.

[25] S. Burger, et al.. Dark solitons in Bose–Einstein condensates. Phys. Rev. Lett., 1999, 83(25): 5198-5201.

[26] J. Denschlag, et al.. Generating solitons by phase engineering of a Bose–Einstein condensate. Science, 2000, 287(5450): 97-101.

[27] D. Jaksch, et al.. Cold bosonic atoms in optical lattices. Phys. Rev. Lett., 1998, 81(15): 3108-3111.

[28] M. Greiner, et al.. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature, 2002, 415(6867): 39-44.

[29] B. Eiermann, et al.. Bright Bose–Einstein gap solitons of atoms with repulsive interaction. Phys. Rev. Lett., 2004, 92(23): 230401.

[30] B. B. Baizakov, V. V. Konotop, M. Salerno. Regular spatial structures in arrays of Bose Einstein condensates induced by modulational instability. J. Phys. B, 2002, 35(24): 5105-5119.

[31] L. H. Haddad, L. D. Carr. The nonlinear Dirac equation in Bose–Einstein condensates: II. Relativistic soliton stability analysis. New J. Phys., 2015, 17(6): 063034.

[32] V. S. Bagnato, et al.. Bose–Einstein condensation: twenty years after. Rom. Rep. Phys., 2015, 67(1): 5-50.

[33] D. Mihalache. Multidimensional localized structures in optics and Bose–Einstein condensates: a selection of recent studies. Rom. J. Phys, 2014, 59(3–4): 295-312.

[34] D. Mihalache. Multidimensional localized structures in optical and matter-wave media: a topical survey of recent literature. Rom. Rep. Phys, 2017, 69(1): 403.

[35] L. Salasnich. Bright solitons in ultracold atoms. Opt. Quantum Electron., 2017, 49(12): 409.

[36] P. G. Kevrekidis, et al.. Stability of dark solitons in a Bose–Einstein condensate trapped in an optical lattice. Phys. Rev. A, 2003, 68(3): 035602.

[37] N. G. Parker, et al.. Dynamical instability of a dark soliton in a quasi-one-dimensional Bose–Einstein condensate perturbed by an optical lattice. J. Phys. B, 2004, 37(7): S175-S185.

[38] S.-C. Cheng, T.-W. Chen. Dark gap solitons in exciton-polariton condensates in a periodic potential. Phys. Rev. E, 2018, 97(3): 032212.

[39] X. Ma, O. A. Egorov, S. Schumacher. Creation and manipulation of stable dark solitons and vortices in microcavity polariton condensates. Phys. Rev. Lett., 2017, 118(15): 157401.

[40] M. Qi, et al.. A three-dimensional optical photonic crystal with designed point defects. Nature, 2004, 429(6991): 538-542.

[41] P. V. Braun, S. A. Rinne, F. Garca-Santamara. Introducing defects in 3D photonic crystals: state of the art. Adv. Mater., 2006, 18(20): 2665-2678.

[42] S. A. Rinne, F. Garca-Santamara, P. V. Braun. Embedded cavities and waveguides in three-dimensional silicon photonic crystals. Nat. Photonics, 2008, 2(1): 52-56.

[43] C.-H. Sun, P. Jiang. Photonic crystals: acclaimed defects. Nat. Photonics, 2008, 2(1): 9-11.

[44] J. D.Joannopouloset al., Photonic Crystals: Molding the Flow of Light, Princeton University Press, Princeton, New Jersey (2008).

[45] M. H. Anderson, et al.. Observation of Bose-Einstein condensation in a dilute atomic vapor. Science, 1995, 269(5221): 198-201.

[46] N. G. Vakhitov, A. A. Kolokolov. Stationary solutions of the wave equation in a medium with nonlinearity saturation. Radiophys. Quantum Electron., 1973, 16(7): 783-789.

[47] H. Sakaguchi, B. A. Malomed. Solitons in combined linear and nonlinear lattice potentials. Phys. Rev. A, 2010, 81(1): 013624.

[48] J. Zeng, B. A. Malomed. Two-dimensional solitons and vortices in media with incommensurate linear and nonlinear lattice potentials. Phys. Scripta, 2012, T149: 014035.

[49] J. Shi, J. Zeng. Asymmetric localized states in periodic potentials with a domain-wall-like Kerr nonlinearity. J. Phys. Commun., 2019, 3(3): 035003.

[50] J. Zeng, B. A. Malomed. Two-dimensional intraband solitons in lattice potentials with local defects and self-focusing nonlinearity. J. Opt. Soc. Am. B, 2013, 30(7): 1786-1793.

[51] V. A. Brazhnyi, V. V. Konotop, V. M. Pérez-Garca. Driving defect modes of Bose–Einstein condensates in optical lattices. Phys. Rev. Lett., 2006, 96(6): 060403.

[52] V. A. Brazhnyi, V. V. Konotop, V. M. Pérez-Garca. Defect modes of a Bose–Einstein condensate in an optical lattice with a localized impurity. Phys. Rev. A, 2006, 74(2): 023614.

[53] V. A. Brazhnyi, M. Salerno. Resonant scattering of matter-wave gap solitons by optical lattice defects. Phys. Rev. A, 2011, 83(5): 053616.

[54] N. Dror, B. A. Malomed, J. Zeng. Domain walls and vortices in linearly coupled systems. Phys. Rev. E, 2011, 84(4): 046602.

[55] Y. V. Kartashov, B. A. Malomed, L. Torner. Solitons in nonlinear lattices. Rev. Mod. Phys., 2011, 83(1): 247-305.

[56] J. Zeng, B. A. Malomed. Stabilization of one-dimensional solitons against the critical collapse by quintic nonlinear lattices. Phys. Rev. A, 2012, 85(2): 023824.

[57] X. Gao, J. Zeng. Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices. Front. Phys., 2018, 13(1): 130501.

[58] J. Shi, J. Zeng, B. A. Malomed. Suppression of the critical collapse for one-dimensional solitons by saturable quintic nonlinear lattices. Chaos, 2018, 28(7): 075501.

[59] L. Zeng, et al.. Purely Kerr nonlinear model admitting flat-top solitons. Opt. Lett., 2019, 44(5): 1206-1209.

[60] C. Chin, et al.. Feshbach resonances in ultracold gases. Rev. Mod. Phys., 2010, 82(2): 1225-1286.

[61] G. Theocharis, et al.. Ring dark solitons and vortex necklaces in Bose–Einstein condensates. Phys. Rev. Lett., 2003, 90(12): 120403.

[62] D. N. Christodoulides, F. Lederer, Y. Silberberg. Discretizing light behaviour in linear and nonlinear waveguide lattices. Nature, 2003, 424(6950): 817-823.

[63] I. L. Garanovich, et al.. Light propagation and localization in modulated photonic lattices and waveguides. Phys. Rep., 2012, 518(1): 1-79.