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Dynamics of light bullets in inhomogeneous cubic-quintic-septimal nonlinear media with \({\varvec{{\mathcal {PT}}}}\)-symmetric potentials

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Abstract

A (3+1)-dimensional nonlinear Schrödinger equation with variable-coefficient dispersion/diffraction and cubic-quintic-septimal nonlinearities is studied, two families of analytical light bullet solutions with two types of \({{\mathcal {PT}}}\)-symmetric potentials are obtained. The coefficient of the septimal nonlinear term strongly influences the form of light bullet. The direct numerical simulation indicates that light bullet solutions in different cubic-quintic-septimal nonlinear media exhibit different property of stability, and under different \({\mathcal {PT}}\)-symmetric potentials they also show different stability against white noise. These stabilities of evolution originate from subtle interplay among dispersion, diffraction, nonlinearity and \({\mathcal {PT}}\)-symmetric potential. Moreover, compression and expansion of light bullets in the hyperbolic dispersion/diffraction system and periodic modulation system are investigated numerically. The evolution of light bullet in periodic modulation system is more stable than that in the hyperbolic dispersion/diffraction system.

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References

  1. Biswas, A., Khan, K.R., Milovic, D., Belic, M.: Bright and dark solitons in optical metamaterials. Optik 125, 3299–3302 (2014)

    Article  Google Scholar 

  2. Zhou, Q., Liu, L., Liu, Y., Yu, H., Yao, P., Wei, C., Zhang, H.: Exact optical solitons in metamaterials with cubic-quintic nonlinearity and third-order dispersion. Nonlinear Dyn. 80, 1365–1371 (2015)

    Article  Google Scholar 

  3. Dai, C.Q., Wang, Y.Y.: Controllable combined Peregrine soliton and Kuznetsov-Ma soliton in PT-symmetric nonlinear couplers with gain and loss. Nonlinear Dyn 80, 715–721 (2015)

    Article  MathSciNet  Google Scholar 

  4. Zhu, H.P., Pan, Z.H.: Vortex soliton in (2+1)-dimensional PT-symmetric nonlinear couplers with gain and loss. Nonlinear Dyn. 83, 1325–1330 (2016)

    Article  MathSciNet  Google Scholar 

  5. Dai, C.Q., Wang, Y.Y.: Spatiotemporal localizations in (3+1)-dimensional PT-symmetric and strongly nonlocal nonlinear media. Nonlinear Dyn 83, 2453C2459 (2016)

    Article  MathSciNet  Google Scholar 

  6. Liu, W.J., Pang, L.H., Han, H.N., Chen, H., Lei, M., Yuan, P.G., Wei, Z.Y.: Generation of dark solitons in erbium-doped fiber lasers based Sb \(_2\)Te\(_3\) saturable absorbers. Opt. Express 23, 26023–26031 (2015)

    Article  Google Scholar 

  7. Dai, C.Q., Xu, Y.J.: Exact solutions for a Wick-type stochastic reaction Duffing equation. Appl. Math. Model. 39, 7420–7426 (2015)

    Article  MathSciNet  Google Scholar 

  8. Zhou, Q., Zhu, Q.: Optical solitons in medium with parabolic law nonlinearity and higher order dispersion. Waves Random Complex Media 25, 52–59 (2015)

    Article  Google Scholar 

  9. Xu, S.L., Petrovic, N., Belic, M.R.: Exact solutions of the (3+1)-dimensional cubic-quintic nonlinear Schrodinger equation with variable coefficients. Nonlinear Dyn. 81, 574–579 (2016)

    Google Scholar 

  10. Zhou, Q.: Optical solitons in the parabolic law media with high-order dispersion. Optik 125, 5432–5435 (2014)

    Article  Google Scholar 

  11. Aitchison, J.S., Weiner, A.M., Silberberg, Y., Oliver, M.K., Jackel, J.L., Leaird, D.E., Vogel, E.M., Smith, P.W.E.: Observation of spatial optical solitons in a nonlinear glass waveguide. Opt. Lett. 15, 471–474 (1990)

    Article  Google Scholar 

  12. Chung, Y., Lushnikov, P.M.: Strong collapse turbulence in a quintic nonlinear Schrodinger equation. Phys. Rev. E 84, 036602 (2011)

    Article  Google Scholar 

  13. Rasmussen, J.J., Rypdal, K.: Blow-up in nonlinear Schrodinger equations-I, a general review. Phys. Scr. 33, 481 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  14. Skarka, V., Berezhiani, V.I., Miklaszewski, R.: Spatiotemporal soliton propagation in saturating nonlinear optical media. Phys. Rev. E 56, 1080–1087 (1997)

    Article  Google Scholar 

  15. Reyna, A.S., Jorge, K.C., de Araujo, C.B.: Two-dimensional solitons in a quintic-septimal medium. Phys. Rev. A 90, 063835 (2014)

    Article  Google Scholar 

  16. Bender, C.M., Boettcher, S.: Real spectra in non-Hermitian Hamiltonians having PT-symmetry. Phys. Rev. Lett. 80, 5243–5246 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  17. Musslimani, Z.H., Makris, K.G., El-Ganainy, R., Christodoulides, D.N.: Optical solitons in PT periodic potentials. Phys. Rev. Lett. 100, 030402 (2008)

    Article  MATH  Google Scholar 

  18. Chen, Y.X.: Stable 2D localized modes in anisotropic media with harmonic and PT-symmetric potentials. Commun Nonlinear Sci Numer Simulat 22, 1313–1321 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  19. Chen, Y.X.: Sech-type and Gaussian-type light bullet solutions to the generalized (3+1)-dimensional cubic-quintic Schrödinger equation in \({\cal{PT}}\)-symmetric potentials. Nonlinear Dyn. 79, 427–436 (2015)

    Article  MathSciNet  Google Scholar 

  20. Wang, Y.Y., Dai, C.Q., Wang, X.G.: Stable localized spatial solitons in PT-symmetric potentials with power-law nonlinearity. Nonlinear Dyn. 77, 1323–1330 (2014)

    Article  MathSciNet  Google Scholar 

  21. Belyaeva, T.L., Serkin, V.N., Agüero, M.A., Hernandez-Tenorio, C., Kovachev, L.M.: Hidden features of the soliton adaptation law to external potentials: optical and matter-wave 3D nonautonomous soliton bullets. Laser Phys. 21, 258–263 (2011)

    Article  Google Scholar 

  22. Reyna, A.S., Malomed, B.A., de Araújo, C.B.: Stability conditions for one-dimensional optical solitons in cubic-quintic-septimal media. Phys. Rev. A 92, 033810 (2015)

    Article  Google Scholar 

  23. Abramowitz, M., Stegun, I.A.: “Chapter 15”, Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover, New York (1965)

    MATH  Google Scholar 

  24. Da Silva, M.G., Nobrega, K.Z., Sombra, A.S.B.: Analysis of soliton switching in dispersion-decreasing fiber couplers. Opt. Commun. 171, 351–364 (1999)

    Article  Google Scholar 

  25. Ganathy, R., Kuriakose, V.C.: Soliton pulse compression in a dispersion decreasing elliptic birefringent fiber with effective gain and effective phase modulation. J. Nonlin. Opt. Phys. Mater. 11, 185–195 (2002)

    Article  Google Scholar 

  26. Vinoj, M.N., Kuriakose, V.C.: Generation of pedestal-free ultrashort soliton pulses and optimum dispersion profile in real dispersion-decreasing fibre. J. Opt. A 6, 63–70 (2004)

    Article  Google Scholar 

  27. Dai, C.Q., Wang, X.G., Zhou, G.Q.: Stable light-bullet solutions in the harmonic and parity-time-symmetric potentials. Phys. Rev. A 89, 013834 (2014)

    Article  Google Scholar 

  28. Midya, B., Roychoudhury, R.: Nonlinear localized modes in PT-symmetric Rosen-Morse potential wells. Phys. Rev. A 87, 045803 (2013)

    Article  Google Scholar 

  29. Belic, M., Zhong, W.P., Petrovic, N., Xie, R.H., Chen, G.: Analytical light bullet solutions to the generalizede (3+1)-dimensio nal nonlinear Schrodinger equation. Phys. Rev. Lett. 101, 123904 (2008)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant Nos. LY17F050011 and LY17A040011), the National Natural Science Foundation of China (Grant Nos. 11375007, 11574271 and 11404289). Dr. Chao-Qing Dai is also sponsored by the Foundation of New Century “151 Talent Engineering” of Zhejiang Province of China and Youth Top-notch Talent Development and Training Program of Zhejiang A&F University. Dr. Rui-Pin Chen is also sponsored by the Science Research Foundation of Zhejiang Sci-Tech University (ZSTU) under Grant No. 14062078-Y.

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Authors and Affiliations

  1. School of Sciences, Zhejiang A&F University, Lin’an, 311300, Zhejiang, People’s Republic of China

    Chao-Qing Dai, Yue-Yue Wang & Yan Fan

  2. Department of Physics, Zhejiang Sci-Tech University, Hangzhou, 310018, Zhejiang, People’s Republic of China

    Rui-Pin Chen

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  1. Chao-Qing Dai
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  2. Rui-Pin Chen
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  4. Yan Fan
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Correspondence to Chao-Qing Dai.

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Dai, CQ., Chen, RP., Wang, YY. et al. Dynamics of light bullets in inhomogeneous cubic-quintic-septimal nonlinear media with \({\varvec{{\mathcal {PT}}}}\)-symmetric potentials. Nonlinear Dyn 87, 1675–1683 (2017). https://doi.org/10.1007/s11071-016-3143-0

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