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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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, 35, 5105-5119(2002).

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

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

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

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

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

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

[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, 37, S175-S185(2004).

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

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

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

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

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

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

[44] J. D. Joannopoulos et al. Photonic Crystals: Molding the Flow of Light(2008).

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

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

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

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

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

[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, 30, 1786-1793(2013).

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

[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, 74, 023614(2006).

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

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

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

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

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

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

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

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

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

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

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