[1] KORTEWEG D J, DEVRIES F. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves[J]. Philosophical Magazine, 39, 422-443(1895).

[2] COSTA A, OSBORNE A R, RESIO D T et al. Soliton turbulence in shallow water ocean surface waves[J]. Physical Review Letters, 113, 108501(2014).

[3] CHANG W, HÖLZER P, TRAVERS J C et al. Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber[J]. Optics Letters, 38, 2984-2987(2013).

[4] [4] AGRAWL G P. Nonlinear Fiber Optics [M]. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000: 195211.

[5] WANG D S, LU X. Numerical simulation of propagation properties of optical soliton and quasi-soliton[J]. Infrared and Laser Engineering, 40, 511-514, 524(2011).

[6] JI X M, JIANG Q C, LIU J S. Grey screening-photovoltaic spatial soliton in two-photon photorefractive crystals[J]. Infrared and Laser Engineering, 40, 36-40(2011).

[7] JI X M, JIANG Q C, SU Y L. et al. Temporal behavior of the screening grey spatial solitons in one-photon centrosymmetric and non-centrosymmetric photorefractive crystals[J]. Infrared and Laser Engineering, 42, 63-68(2013).

[8] GUO Y Q. Family of Super-Gaussian beams spatial optical solitons in sub-strongly non-local nonlinear media[J]. Acta Photonica Sinica, 36, 1414-1417(2007).

[9] ZHANG X P, LIU Y W. Analytical solution of high-order mode spatial optical solitons propagating in the strong nonlocal media[J]. Acta Photonica Sinica, 37, 2418-2421(2008).

[10] SNYDER A W, MITCHELL D J. Accessible solitons[J]. Science, 276, 1538-1541(1997).

[11] XIE Y Q, GUO Q. Spatial photosoliton interactions in non-local Kerr media[J]. Acta Physica Sinica, 53, 5(2004).

[12] ZHU Y Q, HU W. Interaction between optical solitons in nonlocal Kerr media[J]. Acta Optica Sinica, 35, 243-249(2015).

[13] SHEN M, SHI J, WANG Q. Incoherent accessible white-light solitons in strongly nonlocal Kerr media[J]. Physical Review E, 74, 027601(2006).

[14] GE L, SHEN M, ZANG T et al. Stability of optical solitons in parity-time-symmetric optical lattices with competing cubic and quintic nonlinearities[J]. Physical Review E, 91, 023203(2015).

[15] HAO L L, HOU C F, MU H W. Coherently coupled soliton pairs in biased two-photon photorefractive crystals with both linear and quadratic electro-optic effects[J]. Infrared and Laser Engineering, 45, S108001(2016).

[16] HAO L L, WANG Q, TANG H X et al. Low-amplitude coherently coupled spatial soliton pairs due to both the linear and quadratic electro-optic effects[J]. Infrared and Laser Engineering, 48, S106006(2019).

[17] MU Y N, LI Y J, CHEN W J. Theoretical study on interaction effect of self-accelerating beams in a biased photovoltaic photorefractive crystal[J]. Infrared and Laser Engineering, 20220096.(202251).

[18] ASSANTO G, KARPIERZ M A. Nematicons: self-localised beams in nematic liquid crystals[J]. Liquid Crystals, 36, 1161-1172(2009).

[19] PICCARDI A, RESIDORI S, ASSANTO G. Nonlocal soliton scattering in random potentials[J]. Journal of Optics, 18, 07LT01(2016).

[20] ROTSCHILD C, SEGEV M, XU Z et al. Two-dimensional multipole solitons in nonlocal nonlinear media[J]. Optics Letters, 31, 3312-3314(2006).

[21] ROTSCHILD C, ALFASSI B, COHEN O et al. Long-range interactions between optical solitons[J]. Nature Physics, 2, 769-774(2006).

[22] WANG Q, LI J Z, WANG X H. Spatial optical soliton in (1+2)-dimensional synthetic nonlocal nonlinear media[J]. Optik, 126, 3567-3569(2017).

[23] WANG Q, DENG Z Z. Elliptic solitons in (1+2)-dimensional anisotropic nonlocal nonlinear fractional schrdinger equation[J]. IEEE Photonics Journal, 11, 1-8(2019).

[24] WANG Q, LI J Z, GAO X H et al. Nonlocal logarithmic nonlinear optical soliton[J]. Optik, 172, 571-577(2018).

[25] JUNG P S, KROLIKOWSKI W, LAUDYN U A et al. Supermode spatial optical solitons in liquid crystals with competing nonlinearities[J]. Physical Review A, 95, 023820(2017).

[26] JUNG P S, KROLIKOWSKI W, LAUDYN U A et al. Semi-analytical approach to supermode spatial solitons formation in nematic liquid crystals[J]. Optics Express, 25, 23893-23898(2017).

[27] JUNG P S, KARPIER M, TRIPPENBACH M et al. Supermode spatial solitons via competing nonlocal nonlinearities[J]. Photonics Letters of Poland, 10, 33-35(2018).

[28] PU S Z, LI Y J. Bright soliton in liquid crystal with competing nonlocal nonlinearities[J]. Acta Photonica Sinica, 48, 1048002(2019).

[29] CYPRYCH K, JUNG P S, IZDEBSKAYA Y et al. Anomalous interaction of spatial solitons in nematic liquid crystals[J]. Optics Letters, 44, 267-270(2019).

[30] RAMANIUK A, JUNG P S, CHRISTODOULIDES D N et al. Absorption-mediated stabilization of nonlinear propagation of vortex beams in nematic liquid crystals[J]. Optics Communications, 451, 338-344(2019).

[31] PU S, CHEN M, LI Y et al. Solitons in liquid crystals with competing nonlinearities[J]. Optics Communications, 450, 78-86(2019).

[32] PU S, LIANG Y, REN S et al. Dark solitons in liquid crystals with competing re-orientational and thermal nonlocal nonlinearities[J]. JOSA B, 41, 969-975(2024).

[33] JUNG P S, PYRIALAKOS G G, PILKA J et al. Stable fundamental two-dimensional solitons in media with competing nonlocal interactions[J]. Chaos, Solitons & Fractals, 171, 113381(2023).

[34] DU B, GE L, SHEN M. Two-dimensional modulation instability and higher-order soliton clusters in nematic liquid crystals with competing re-orientational and thermal nonlocal nonlinearities[J]. Results in Physics, 57, 107433(2024).

[35] WANG X H, GUO Q, XIE Y Q. Propagation properties the paraxial Gaussian beams in strongly nonlocal media[J]. Acta Optica Sinica, 25, 7.(2005).

[36] WANG X H, GUO Q, XIE Y Q. Analysis of Gaussian beam parameters evolution law in strongly nonlocal media[J]. Chinese Journal of Lasers, 32, 1059-1062.(2005).

[37] DU Y, ZHOU Z, TIAN H et al. Bright solitons and repulsive in-phase interaction in media with competing nonlocal Kerr nonlinearities[J]. Journal of Optics, 13, 015201(2010).

[38] ESBENSEN B K, WLOTZKA A, BACHE M et al. Modulational instability and solitons in nonlocal media with competing nonlinearities[J]. Physical Review A, 84, 05385(2011).