[1] Liu WM, KengneE. Schrödinger equations in nonlinear systems[M]. Singapore: Springer, 2019.

[2] Kevrekidis PG, Frantzeskakis DJ, Carretero-GonzálezR. The defocusing nonlinear Schrödinger equation[M]. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2015.

[3] FibichG. The nonlinear Schrödinger equation: singular solutions and optical collapse[M]. New York: Springer, 2015.

[4] Chen ZJ. Solutions of nonlinear Schrödinger systems[M]. Heidelberg: Springer, 2015.

[5] SulemC, Sulem PL. The nonlinear Schrödinger equation: self-focusing and wave collapse[M]. New York: Springer, 2004.

[6] DauxoisT, PeyrardM. Physics of solitons[M]. Cambridge: Cambridge University Press, 2006.

[7] Williams MC. Solitons[M]. Hauppauge: Nova Science Publishers, 2013.

[8] Hu X H, Zhang X F, Zhao D, et al. Dynamics and modulation of ring dark solitons in two-dimensional Bose-Einstein condensates with tunable interaction[J]. Physical Review A, 2009, 79(2): 023619.

[9] Liang Z X, Zhang Z D, Liu W M. Dynamics of a bright soliton in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic potential[J]. Physical Review Letters, 2005, 94(5): 050402.

[10] Wu B, Liu J, Niu Q. Controlled generation of dark solitons with phase imprinting[J]. Physical Review Letters, 2002, 88(3): 034101.

[11] Huang G X, Makarov V A, Velarde M G. Two-dimensional solitons in Bose-Einstein condensates with a disk-shaped trap[J]. Physical Review A, 2003, 67(2): 023604.

[12] Triki H, Zhou Q, Liu W J. W-shaped solitons in inhomogeneous cigar-shaped Bose-Einstein condensates with repulsive interatomic interactions[J]. Laser Physics, 2019, 29(5): 055401.

[13] Brand J, Reinhardt W P. Solitonic vortices and the fundamental modes of the “snake instability”: possibility of observation in the gaseous Bose-Einstein condensate[J]. Physical Review A, 2002, 65(4): 043612.

[14] Donadello S, Serafini S, Tylutki M, et al. Observation of solitonic vortices in Bose-Einstein condensates[J]. Physical Review Letters, 2014, 113(6): 065302.

[15] Ku M J, Ji W J, Mukherjee B, et al. Motion of a solitonic vortex in the BEC-BCS crossover[J]. Physical Review Letters, 2014, 113(6): 065301.

[16] Sakaguchi H. New models for multi-dimensional stable vortex solitons[J]. Frontiers of Physics, 2019, 14: 12301.

[17] Anderson B P, Haljan P C, Regal C A, et al. Watching dark solitons decay into vortex rings in a Bose-Einstein condensate[J]. Physical Review Letters, 2001, 86(14): 2926-2929.

[18] Yang S J, Wu Q S, Zhang S N, et al. Generating ring dark solitons in an evolving Bose-Einstein condensate[J]. Physical Review A, 2007, 76(6): 063606.

[19] Becker C, Sengstock K, Schmelcher P, et al. Inelastic collisions of solitary waves in anisotropic Bose-Einstein condensates: sling-shot events and expanding collision bubbles[J]. New Journal of Physics, 2013, 15(11): 113028.

[20] Qi Y, Sun H, Niu Y, et al. Ultraslow solitons and soliton pairs in asymmetric quantum wells[J]. Chinese Journal of Lasers, 2009, 36(s1): 96-99.

[21] Dutta S, Mueller E J. Collective modes of a soliton train in a fermi superfluid[J]. Physical Review Letters, 2017, 118(26): 260402.

[22] Herink G, Kurtz F, Jalali B, et al. Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules[J]. Science, 2017, 356(6333): 50-54.

[23] Spuntarelli A, Carr L D, Pieri P, et al. Gray solitons in a strongly interacting superfluid Fermi gas[J]. New Journal of Physics, 2011, 13(3): 035010.

[24] Reichl M D, Mueller E J. Core filling and snaking instability of dark solitons in spin-imbalanced superfluid Fermi gases[J]. Physical Review A, 2017, 95(5): 053637.

[25] Burger S, Bongs K, Dettmer S, et al. Dark solitons in Bose-Einstein condensates[J]. Physical Review Letters, 1999, 83(25): 5198-5201.

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

[27] Khaykovich L, Schreck F, Ferrari G, et al. Formation of a matter-wave bright soliton[J]. Science, 2002, 296(5571): 1290-1293.

[28] Kevrekidis PG, Frantzeskakis DJ, Carretero-GonzálezR. Emergent nonlinear phenomena in Bose-Einstein condensates[M]. Heidelberg: Springer, 2008.

[29] Zhang X F, Hu X H, Liu X X, et al. Vector solitons in two-component Bose-Einstein condensates with tunable interactions and harmonic potential[J]. Physical Review A, 2009, 79(3): 033630.

[30] Liu X X, Pu H, Xiong B, et al. Formation and transformation of vector solitons in two-species Bose-Einstein condensates with a tunable interaction[J]. Physical Review A, 2009, 79(1): 013423.

[31] 赵岩, 宋丽军, 王艳. 多组分耦合非线性薛定谔方程的3-孤子解及其相互作用[J]. 光学学报, 2019, 39(4): 0419001.

    Zhao Y, Song L J, Wang Y. 3-soliton solutions of multi-component coupled nonlinear Schrödinger equation and their interaction[J]. Acta Optica Sinica, 2019, 39(4): 0419001.

[32] Köhler T. Three-body problem in a dilute Bose-Einstein condensate[J]. Physical Review Letters, 2002, 89(21): 210404.

[33] Huang T W, Zhou C T, He X T. Propagation of femtosecond terawatt laser pulses in N2 gas including higher-order Kerr effects[J]. AIP Advances, 2012, 2(4): 042190.

[34] Kolomeisky E B, Newman T J, Straley J P, et al. Low-dimensional Bose liquids: beyond the Gross-Pitaevskii approximation[J]. Physical Review Letters, 2000, 85(6): 1146-1149.

[35] Zhan C L, Zhang D Q, Zhu D B, et al. Third- and fifth-order optical nonlinearities in a new stilbazolium derivative[J]. Journal of the Optical Society of America B, 2002, 19(3): 369-375.

[36] 杜英杰, 杨战营, 谢小涛, 等. 电磁感应透明的高阶非线性效应对光孤子的影响[J]. 光学学报, 2015, 35(2): 0227002.

    Du Y J, Yang Z Y, Xie X T, et al. Influence of higher nonlinearity to optical solitons in electromagnetically induced transparency medium[J]. Acta Optica Sinica, 2015, 35(2): 0227002.

[37] Vakhitov N G, Kolokolov A A. Stationary solutions of the wave equation in a medium with nonlinearity saturation[J]. Radiophysics and Quantum Electronics, 1973, 16(7): 783-789.

[38] Weinstein M I. Lyapunov stability of ground states of nonlinear dispersive evolution equations[J]. Communications on Pure and Applied Mathematics, 1986, 39(1): 51-67.

[39] ViolaC. An introduction to special functions[M]. Cham: Springer, 2016.

[40] Seaborn JB. Hypergeometric functions and their applications[M]. New York: Springer, 1991.

[41] Antezza M, Dalfovo F, Pitaevskii L P, et al. Dark solitons in a superfluid Fermi gas[J]. Physical Review A, 2007, 76(4): 043610.

[42] Pethick CJ, SmithH. Bose-Einstein condensation in dilute gases[M]. 2nd ed. Cambridge: Cambridge University Press, 2008.

[43] PitaevskiiL, StringariS. Bose-Einstein condensation and superfluidity[M]. Oxford: Oxford University Press, 2016.