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Cosine-Gaussian breathers controlled by the initial conditions in highly nonlocal media

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Abstract

The study delves into the behavior of cos-Gaussian breathers navigating through a highly nonlocal medium, with a spotlight on their width and intensity variations under different parameter adjustments. The mathematical formulas describing the characteristics of cos-Gaussian beams have been derived. By controlling the parameters, the transverse width of cos-Gaussian beams can exhibit various variations, reflecting various mode transformations. We scrutinized how alterations in cosine parameters, offset distance, and initial energy manifest in the breather’s width and shape during propagation. Our observations underscore the significant influence of these parameters on the dynamic evolution and morphology of cos-Gaussian breathers, thereby unveiling the potential application of using parameters to control the dynamic characteristics of cos-Gaussian beam transmission.

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References

  • Bi, K., Hao, H.Q., Zhang, J.W., Guo, R.: Soliton, breather-like and dark-soliton-breather-like solutions for the coupled long-wave-short-wave system. Nonlinear Dyn. 108, 543–554 (2022)

    Article  Google Scholar 

  • Dai, Z.P., Yang, Z.J., Zhang, S.M., Pang, Z.G., You, K.M.: Transversal reverse transformation of anomalous hollow beams in strongly isotropic nonlocal media. Chin. Phys. B 23, 074208 (2014)

    Article  ADS  Google Scholar 

  • Dai, Z.P., Zeng, Q., Shen, S., Yang, Z.J.: Periodically revived elliptical Cos-Gaussian solitons and breathers in nonlocal nonlinear Schrödinger equation. Results Phys. 23, 104055 (2021)

    Article  Google Scholar 

  • Dai, Z.P., Wang, Y.J., Wang, Y.C., Yang, Z.J., Pang, Z.G.: Propagation properties of controllable anomalous hollow beams in strongly nonlocal nonlinear media. Results Phys. 42, 105951 (2022)

    Article  Google Scholar 

  • Deng, D., Guo, Q.: Ince-Gaussian solitons in strongly nonlocal nonlinear media. Opt. Lett. 32(21), 3206–3208 (2007)

    Article  ADS  Google Scholar 

  • Deng, B.J., Hao, H.Q.: Breathers, rogue waves and semi-rational solutions for a generalized Heisenberg ferromagnet equation. Appl. Math. Lett. 140, 108550 (2023)

    Article  MathSciNet  Google Scholar 

  • Guo, Q., Luo, B., Yi, F., Chi, S., Xie, Y.: Large phase shift of nonlocal optical spatial solitons. Phys. Rev. E 69(1), 016602 (2004)

    Article  ADS  Google Scholar 

  • Guo, J.L., Yang, Z.J., Song, L.M., Pang, Z.G.: Propagation dynamics of tripole breathers in nonlocal nonlinear media. Nonlinear Dyn. 101, 1147–1157 (2020)

    Article  Google Scholar 

  • Izdebskaya, Y.V., Desyatnikov, A.S., Kivshar, Y.S.: Self-induced mode transformation in nonlocal nonlinear media. Phys. Rev. Lett. 111, 123902 (2013)

    Article  ADS  Google Scholar 

  • Li, X.L., Guo, R.: Interactions of localized wave structures on periodic backgrounds for the coupled Lakshmanan-Porsezian-Daniel equations in birefringent optical fibers. Ann. Phys. 535, 2200472 (2022)

    Article  Google Scholar 

  • Li, J., Yang, Z.J., Zhang, S.M.: Periodic collision theory of multiple Cosine-Hermite-Gaussian solitons in Schrödinger equation with nonlocal nonlinearity. Appl. Math. Lett. 140, 108588 (2023)

    Article  Google Scholar 

  • Liang, G., Hong, W., Guo, Q.: Spatial solitons with complicated structure in nonlocal nonlinear media. Opt. Express 25, 28784–28793 (2016)

    Article  ADS  Google Scholar 

  • Liu, D.S., Gao, Y.X., Fan, D.Y., Zhang, L.F.: Higher-charged vortex solitons in harmonic potential. Chaos Solitons Fractals 171, 113422 (2023)

    Article  Google Scholar 

  • 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(4), 043815 (2008)

    Article  ADS  Google Scholar 

  • Lu, D., Zhan, Q., Duan, Q., Hu, W.: Power-variation-induced three-dimensional nonuniform scaling of beams in strongly nonlocal nonlinear media. Phys. Rev. A 87, 023815 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Maucher, F., Pohl, T., Skupin, S., Krolikowski, W.: Self-organization of light in optical media with competing nonlinearities. Phys. Rev. Lett. 116, 163902 (2016)

    Article  ADS  Google Scholar 

  • Rotschild, C., Alfassi, B., Cohen, O., Segev, M.: Long-range interactions between optical solitons. Nat. Phys. 2, 769–774 (2006)

    Article  Google Scholar 

  • Shen, S., Yang, Z.J., Li, X.L., Zhang, S.M.: Periodic propagation of complex-valued hyperbolic-Cosine-Gaussian solitons and breathers with complicated light field structure in strongly nonlocal nonlinear media. Commun. Nonlinear Sci. Numer. Simul. 103, 106005 (2021)

    Article  MathSciNet  Google Scholar 

  • Shen, S., Yang, Z.J., Wang, H., Pang, Z.G.: Nonlinear propagation dynamics of lossy tripolar breathers in nonlocal nonlinear media. Nonlinear Dyn. 110(2), 1767–1776 (2022)

    Article  Google Scholar 

  • Shen, S., Yang, Z.J., Pang, Z.G., Ge, Y.R.: The complex-valued astigmatic Cosine-Gaussian soliton solution of the nonlocal nonlinear Schrödinger equation and its transmission characteristics. Appl. Math. Lett. 125, 107755 (2022)

    Article  Google Scholar 

  • Snyder, A.W., Mitchell, D.J.: Accessible solitons. Science 276, 1538–1541 (1997)

    Article  Google Scholar 

  • Song, L., Yang, Z., Li, X., Zhang, S.: Controllable Gaussian-shaped soliton clusters in strongly nonlocal media. Opt. Express 26, 19182–19198 (2018)

    Article  ADS  Google Scholar 

  • Song, L., Yang, Z., Zhang, S., Li, X.: Spiraling anomalous vortex beam arrays in strongly nonlocal nonlinear media. Phys. Rev. A 99, 063817 (2019)

    Article  ADS  Google Scholar 

  • Song, L.M., Yang, Z.J., Li, X.L., Zhang, S.M.: Coherent superposition propagation of Laguerre-Gaussian and Hermite-Gaussian solitons. Appl. Math. Lett. 102, 106114 (2020)

    Article  MathSciNet  Google Scholar 

  • Sun, Z.Y., Deng, D., Pang, Z.G., Yang, Z.J.: Nonlinear transmission dynamics of mutual transformation between array modes and hollow modes in elliptical Sine-Gaussian cross-phase beams. Chaos Solitons Fractals 178, 114398 (2024)

    Article  MathSciNet  Google Scholar 

  • Wang, Q., Dumitru, M., Belic, M.R., Zhang, L., Ke, L., Zeng, L.: Controllable propagation paths of gap solitons. Opt. Lett. 47(5), 1041–1044 (2022)

    Article  ADS  Google Scholar 

  • Wang, Q., Mihalache, D., Belić, M.R., Zeng, L., Lin, J.: Spiraling Laguerre-Gaussian solitons and arrays in parabolic potential wells. Opt. Lett. 48(16), 4233–4236 (2023)

    Article  ADS  Google Scholar 

  • Yang, Z.J., Zhang, S.M., Li, X.L., Pang, Z.G., Bu, H.X.: High-order revivable complex-valued hyperbolic-Sine-Gaussian solitons and breathers in nonlinear media with a spatial nonlocality. Nonlinear Dyn. 94, 2563–2573 (2018)

    Article  Google Scholar 

  • Yang, Z.J., Bu, H.X., Wang, Y.B., Li, X.L., Zhang, S.M.: Anomalous transverse transformation of astigmatic four-petal Gaussian beams in isotropic nonlocal nonlinear media. Results Phys. 10, 320–322 (2018)

    Article  ADS  Google Scholar 

  • Zhang, Y.Q., Liu, X., Belic, R.M., Zhong, W.P., Wen, F., Zhang, Y.P.: Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential. Opt. Lett. 16, 3786–3789 (2015)

    Article  ADS  Google Scholar 

  • Zhang, Y.Q., Belic, M.R., Zhang, L., Zhong, W.P., Zhu, D.Y., Wang, R.M., Zhang, Y.P.: Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential. Opt. Express 23, 10467–10480 (2015)

    Article  ADS  Google Scholar 

  • Zhang, L.F., Li, H.Z., Liu, Z., Zhang, J., Cai, W.Y., Gao, Y.X., et al.: Controlling Cosine-Gaussian beams in linear media with quadratic external potential. Opt. Express 29, 5128–5140 (2021)

    Article  ADS  Google Scholar 

  • Zhang, S., Zhou, Z., Zhou, Y., Xu, H., Yuan, Y., Han, Y., Zhou, Z., Yao, B., Qu, J.: Twisted Gaussian schell-model breathers and solitons in strongly nonlocal nonlinear media. Opt. Express 30, 32019–32030 (2022)

    Article  ADS  Google Scholar 

  • Zhang, L., Ke, L., Guo, Y., Zhang, X., Wang, Q.: Even and odd Laguerre-Gaussian chaoticons in nematic liquid crystal. Chaos Solitons Fractals 173, 113640 (2023)

    Article  MathSciNet  Google Scholar 

  • Zou, Z.F., Guo, R.: The Riemann-Hilbert approach for the higher-order Gerdjikov-Ivanov equation, soliton interactions and position shift. Commun. Nonlinear Sci. Numer. Simul. 124, 107316 (2023)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was funded by the National Natural Science Foundation of China under Grant No.11874142, the Scientific Research Fund of Hunan Provincial Education Department of China under Grant No.20A071, and the Key Laboratory of Optoelectronic Control and Detection Technology, University of Hunan Province of China.

Funding

The National Natural Science Foundation of China (No. 11874142), The Scientific Research Fund of Hunan Provincial Education Department of China (No. 20A071).

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Authors and Affiliations

  1. College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang, 421002, China

    Peng Pan, Yun-Shi Xu & Zhi-Ping Dai

Authors
  1. Peng Pan
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  2. Yun-Shi Xu
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  3. Zhi-Ping Dai
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Contributions

PP—Software, Validation, Writing—original draft. Y-SX—Validation, Software, Writing—original draft. Z-PD—Conceptualization, Validation, Writing—review & editing.

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Correspondence to Zhi-Ping Dai.

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Pan, P., Xu, YS. & Dai, ZP. Cosine-Gaussian breathers controlled by the initial conditions in highly nonlocal media. Opt Quant Electron 56, 806 (2024). https://doi.org/10.1007/s11082-024-06590-6

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