Shen, Shuang; Yang, Zhen-Jun; Pang, Zhao-Guang; Ge, Yan-Rong The complex-valued astigmatic cosine-Gaussian soliton solution of the nonlocal nonlinear Schrödinger equation and its transmission characteristics. (English) Zbl 1479.78021 Appl. Math. Lett. 125, Article ID 107755, 7 p. (2022). Summary: The complex-valued astigmatic cosine-Gaussian (CVACG) soliton solution of the nonlocal nonlinear Schrödinger equation is presented, and its transmission characteristics in the highly nonlocal nonlinear optical system are discussed. In the highly nonlocal nonlinear optical system, the transverse pattern of CVACG beams is diversified and controllable. In the transmission process, CVACG beams can form spatial solitons and breathers with the special transverse distribution. The two-dimensional transverse equivalent opposite evolution of the second-order moment beam width can be formed. Cited in 5 Documents MSC: 78A60 Lasers, masers, optical bistability, nonlinear optics 35Q55 NLS equations (nonlinear Schrödinger equations) 35C08 Soliton solutions 35B36 Pattern formations in context of PDEs Keywords:nonlocal nonlinear Schrödinger equation; complex-valued soliton solution; nonlinear transmission PDFBibTeX XMLCite \textit{S. Shen} et al., Appl. Math. Lett. 125, Article ID 107755, 7 p. (2022; Zbl 1479.78021) Full Text: DOI References: [1] Snyder, A. W.; Mitchell, D. J., Accessible solitons, Science, 276, 1538 (1997) [2] Rotschild, C.; Cohen, O.; Manela, O.; Segev, M.; Carmon, T., Solitons in nonlinear media with an infinite range of nonlocality: First observation of coherent elliptic solitons and of vortex-ring solitons, Phys. Rev. Lett., 95, Article 213904 pp. (2005) [3] Peccianti, M.; Assanto, G., Nematicons, Phys. Rep., 516, 147-208 (2012) [4] Guo, Q.; Luo, B.; Yi, F.; Chi, S.; Xie, Y., Large phase shift of nonlocal optical spatial solitons, Phys. Rev. E, 69, Article 016602 pp. (2004) [5] Buccoliero, D.; Desyatnikov, A. S.; Krolikowski, W.; Kivshar, Y. S., Spiraling multivortex solitons in nonlocal nonlinear media, Opt. Lett., 33, 198 (2018) [6] Song, L. M.; Yang, Z. J.; Pang, Z. G.; Li, X. L.; Zhang, S. M., Interaction theory of mirror-symmetry soliton pairs in nonlocal nonlinear Schrödinger equation, Appl. Math. Lett., 90, 42-48 (2019) · Zbl 1410.35213 [7] Song, L.; Yang, Z.; Zhang, S.; Li, X., Spiraling anomalous vortex beam arrays in strongly nonlocal nonlinear media, Phys. Rev. A, 99, Article 063817 pp. (2019) [8] Zhong, L.; Li, Y.; Chen, Y.; Hong, W.; Hu, W.; Guo, Q., Chaoticons described by nonlocal nonlinear Schrödinger equation, Sci. Rep., 7, 41438 (2017) [9] Liang, G., Revolving and spinning of optical patterns by two coaxial spiraling elliptic beams in nonlocal nonlinear media, Opt. Express, 27, 14667 (2019) [10] Yang, Z. J.; Zhang, S. M.; Li, X. L.; Pang, Z. G., Variable sinh-Gaussian solitons in nonlocal nonlinear Schrödinger equation, Appl. Math. Lett., 82, 64-70 (2018) · Zbl 1393.78015 [11] Lu, D.; Hu, W.; Zheng, Y.; Liang, Y.; Cao, L.; Lan, S.; Guo, Q., Self-induced fractional Fourier transform and revivable higher-order spatial solitons in strongly nonlocal nonlinear media, Phys. Rev. A, 78, Article 043815 pp. (2008) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.