Skip to main content
Log in

Light bullet in parity-time symmetric potential

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

We derive light bullet solution of a (3\(+\)1)-dimensional nonlinear Schrödinger equation with inhomogeneous diffraction/dispersion and nonlinearity in presence of the parity-time symmetric potential. All characteristic parameters such as amplitude, width, and phase of solution are adapted to the diffraction/dispersion variation. The broadening and compression of LB are studied in the exponential diffraction/dispersion-decreasing medium and the periodic-modulated system. Moreover, the phase changes of light bullet in two kinds of systems are also illustrated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Biswas, A., Khalique, C.M.: Stationary solutions for non-linear dispersive Schrodinger’s equation. Nonlinear Dyn. 63, 623–626 (2011)

    Article  MathSciNet  Google Scholar 

  2. Zhu, H.P.: Nonlinear tunneling for controllable rogue waves in two dimensional graded-index waveguides. Nonlinear Dyn. 72, 873–882 (2013)

    Article  Google Scholar 

  3. Batchelor, G.K.: An introduction to fluid dynamics. Cambridge University Press, Cambridge (2000)

    Book  Google Scholar 

  4. Lu, X., Tian, B., Zhang, H.Q., Xu, T., Li, H.: Generalized (2 +1)-dimensional gardner model: bilinear equations, backlund transformation, lax representation and interaction mechanisms. Nonlinear Dyn. 67, 2279–2290 (2012)

    Article  MathSciNet  Google Scholar 

  5. Serkin, V.N., Hasegawa, A., Belyaeva, T.L.: Nonautonomous solitons in external potentials. Phys. Rev. Lett. 98, 074102 (2007)

    Article  Google Scholar 

  6. Klaiman, S., Gunther, U., Moiseyev, N.: Visualization of branch points in pt-symmetric waveguides. Phys. Rev. Lett. 101, 080402 (2008)

    Article  MathSciNet  Google Scholar 

  7. Makris, K.G., El-Ganainy, R., Christodoulides, D.N., Musslimani, Z.H.: Beam dynamics in pt symmetric optical lattices phys. Rev. Lett. 100, 103904 (2008)

    Article  Google Scholar 

  8. Bender, C.M., Boettcher, S.: Real spectra in non-hermitian hamiltonians having pt-symmetry. Phys. Rev. Lett. 80, 5243–5246 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  9. 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  Google Scholar 

  10. Shi, Z.W., Jiang, X.J., Zhu, X., Li, H.G.: Bright spatial solitons in defocusing kerr media with pt-symmetric potentials. Phys. Rev. A 84, 053855 (2011)

    Article  Google Scholar 

  11. Achilleos, V., Kevrekidis, P.G., Frantzeskakis, D.J.: Carretero-Gonzales, R.: dark solitons and vortices in pt-symmetric nonlinear media from spontaneous symmetry breaking to nonlinear pt phase transitions. Phys. Rev. A 86, 013808 (2012)

    Google Scholar 

  12. Guo, A., Salamo, G.J., Duchesne, D., Morandotti, R., Volatier-Ravat, M., Aimez, V., Siviloglou, G.A., Christodoulides, D.N.: Observation of pt -symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103, 093902 (2009)

    Article  Google Scholar 

  13. Ruter, C.E., Makris, K.G., El-Ganainy, R., Christodoulides, D.N., Segev, M., Kip, D.: Observation of parity-time symmetry in optics. Nature Phys. 6, 192–195 (2010)

    Article  Google Scholar 

  14. Xu, S.L., Belić, M.R., Zhong, W.P.: Three-dimensional spatiotemporal vector solitary waves in coupled nonlinear schrodinger equations with variable coefficients. J. Opt. Soc. Am. B 30, 113–122 (2013)

    Article  Google Scholar 

  15. Zhong, W.P., Belić, M.R., Huang, T.W.: Two-dimensional accessible solitons in pt-symmetric potentials. Nonlinear Dyn. 70, 2027–2034 (2012)

    Article  Google Scholar 

  16. 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 

  17. Serkin, V.N., Hasegawa, A.: Novel soliton solutions of the equation model. Phys. Rev. Lett. 85, 4502–4505 (2000)

    Google Scholar 

  18. Serkin, V.N., Hasegawa, A.: Exactly integrable nonlinear schrodinger equation models with varying dispersion, nonlinearity and gain: application for soliton dispersion management. IEEE J. Sel. Top. Quant. Electron. 8, 418–431 (2002)

    Article  Google Scholar 

  19. Zhong, W.P., Belić, M.R., Huang, T.W.: Solitary waves in the nonlinear schrodinger equation with spatially modulated bessel nonlinearity. J. Opt. Soc. Am. B 30, 1276–1283 (2013)

    Article  Google Scholar 

  20. Dai, C.Q., Wang, Y.Y., Zhang, J.F.: Analytical spatiotemporal localizations for the generalized (3+1)-dimensional nonlinear schrodinger equation. Opt. Lett. 35, 1437–1439 (2010)

    Article  Google Scholar 

  21. Chen, S.H., Dudley, J.M.: Spatiotemporal nonlinear optical self-similarity in three dimensions. Phys. Rev. Lett. 102, 233903 (2009)

    Article  Google Scholar 

  22. 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 

  23. Serkin, V.N., Hasegawa, A., Belyaeva, T.L.: Solitary waves in nonautonomous nonlinear and dispersive systems: nonautonomous solitons. J. Mod. Opt. 57, 1456–1472 (2010)

    Google Scholar 

  24. Zhong, W.P., Xie, R.H., Belić, M.R., Petrović, N., Chen, G., Yi, L.: Exact spatial soliton solutions of the two-dimensional generalized nonlinear schrodinger equation with distributed coefficients. Phys. Rev. A 78, 023821 (2008)

    Article  Google Scholar 

  25. Matuszewski, M., Trippenbach, M., Malomed, B.A., Infeld, E., Skorupski, A.A.: Two-dimensional dispersion-managed light bullets in kerr media. Phys. Rev. E 70, 016603 (2004)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11375007 and 11375079), the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY13F050006), and the Scientific Research and Development Fund of Zhejiang A & F University (Grant No. 2014FR020). Dr. Chao-Qing Dai is also sponsored by the Foundation of New Century “151 Talent Engineering” of Zhejiang Province of China.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chao-Qing Dai.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dai, CQ., Wang, XG. Light bullet in parity-time symmetric potential. Nonlinear Dyn 77, 1133–1139 (2014). https://doi.org/10.1007/s11071-014-1365-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-014-1365-6

Keywords

Navigation