Skip to main content
SpringerLink
Log in

Self-similar azimuthons in strongly nonlocal nonlinear media with \({\varvec{{\mathcal {PT}}}}\)-symmetry

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

Abstract

A (2+1)-dimensional coupled nonlocal nonlinear Schrödinger equation is studied in \({\mathcal {PT}}\)-symmetric nonlocal nonlinear couplers with gain and loss, and approximate self-similar solution of vector rotating azimuthon is obtained. Various structures of rotating azimuthon and soliton cluster are constructed. Moreover, dynamical behaviors of azimuthon and soliton cluster are discussed in the constant diffraction system and the exponential diffraction decreasing waveguide.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Jiang, H.J., Xiang, J.J., Dai, C.Q., Wang, Y.Y.: Nonautonomous bright soliton solutions on continuous wave and cnoidal wave backgrounds in blood vessels. Nonlinear Dyn. 75, 201–207 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. 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 

  3. Dai, C.Q., Zhu, S.Q., Wang, L.L.: Exact spatial similaritons for the generalized (2+1)-dimensional nonlinear Schrodinger equation with distributed coefficients. Europhys. Lett. 92, 24005 (2010)

    Article  Google Scholar 

  4. 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 

  5. 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 

  6. El-Ganainy, R., Makris, K.G., Christodoulides, D.N., Musslimani, Z.H.: Theory of coupled optical PT-symmetric structures. Opt. Lett. 32, 2632–2634 (2007)

    Article  MATH  Google Scholar 

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

    Google Scholar 

  8. 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 

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

    MathSciNet  MATH  Google Scholar 

  10. Wang, Y.Y., Dai, C.Q., Wang, X.G.: Spatiotemporal localized modes in PT-symmetric optical media. Ann. Phys. 348, 289–296 (2014)

    Article  Google Scholar 

  11. 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 

  12. Dai, C.Q., Wang, Y.Y., Zhang, X.F.: Controllable Akhmediev breather and Kuznetsov–Ma soliton trains in PT-symmetric coupled waveguides. Opt. Express 22, 29862 (2014)

    Article  Google Scholar 

  13. Dai, C.Q., Chen, R.P., Zhang, J.F.: Analytical spatiotemporal similaritons for the generalized (3+1)-dimensional Gross–Pitaevskii equation with an external harmonic trap. Opt. Express 44, 862–870 (2011)

    MathSciNet  MATH  Google Scholar 

  14. Zhou, Q., Yu, H., Xiong, X.: Optical solitons in media with time-modulated nonlinearities and spatiotemporal dispersion. Nonlinear Dyn. 80, 983–987 (2015)

    Article  MathSciNet  Google Scholar 

  15. 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 

  16. Li, J.T., Han, J.Z., Du, Y.D., Dai, C.Q.: Controllable behaviors of Peregrine soliton with two peaks in a birefringent fiber with higher-order effects. Phys. Rev. A 82, 1393–1398 (2015)

    MathSciNet  Google Scholar 

  17. Chen, Y.X., Jiang, Y.F., Xu, Z.X., Xu, F.Q.: Nonlinear tunnelling effect of combined Kuznetsov–Ma soliton in (3+1)-dimensional PT-symmetric inhomogeneous nonlinear couplers with gain and loss. Nonlinear Dyn. 82, 589–597 (2015)

    Article  MathSciNet  Google Scholar 

  18. Zhou, Q., Zhu, Q.: Theoretical study of dark solitons in media with competing nonlocal nonlinearities and local quintic nonlinearity. J. Mod. Opt. 61, 1465–1469 (2014)

    Article  Google Scholar 

  19. Zhou, Q., Yao, D., Ding, S., Zhang, Y., Chen, F., Chen, F., Liu, X.: Spatial optical solitons in fifth order and seventh order weakly nonlocal nonlinear media. J. Mod. Opt. 124, 5683–5686 (2013)

    Google Scholar 

  20. Lai, X.J., Jin, M.Z., Zhang, J.F.: Two-dimensional self-similar rotating azimuthons in strongly nonlocal nonlinear media. J. Mod. Opt. 51, 230–242 (2013)

    MathSciNet  Google Scholar 

  21. Zhong, W.P., Belic, M.R.: Three-dimensional optical vortex and necklace solitons in highly nonlocal nonlinear media. Phys. Rev. A 79, 023804 (2009)

    Article  Google Scholar 

  22. Shen, M., Lin, Y.Y., Jeng, C.C., Lee, R.K.: Vortex pairs in nonlocal nonlinear media. J. Opt. 14, 065204 (2012)

    Article  Google Scholar 

  23. Zhou, Q., Yao, D.Z., Liu, X.N., Chen, F., Ding, S.J., Zhang, Y.F., Chen, F.: Exact solitons in three-dimensional weakly nonlocal nonlinear time-modulated parabolic law media. J. Opt. 51, 32–35 (2013)

    Google Scholar 

  24. Desyatnikov, A.S., Sukhorukov, A.A., Kivshar, Y.S.: Azimuthons: spatially modulated vortex solitons. Phys. Rev. Lett. 95(20), 203904 (2005)

    Article  Google Scholar 

  25. Yakimenko, A.I., Zaliznyak, Y.A., Kivshar, Y.S.: Stable vortex solitons in nonlocal self-focusing nonlinear media. Phys. Rev. E 71, 065603 (2005)

    Article  Google Scholar 

  26. Minovich, A., Neshev, D.N., Desyatnikov, A.S., Krolikowski, W., Kivshar, Y.S.: Azimuthons in weakly nonlinear waveguides of different symmetries. Opt. Express 17, 23610 (2009)

    Article  Google Scholar 

  27. Krolikowski, W., Bang, O., Nikolov, N.I., Neshev, D., Wyller, J., Rasmussen, J.J., Edmundson, D.: Modulational instability, solitons, and beam propagation in spatially nonlocal nonlinear media. Opt. Express 6, S288–S294 (2004)

    Google Scholar 

  28. Bang, O., Krolikowski, W., Wyller, J., Rasmussen, J.J.: Collapse arrest and soliton stabilization in nonlocal nonlinear media. Phys. Rev. E 66, 046619 (2002)

    Article  MathSciNet  Google Scholar 

  29. Liang, G., Li, H.G.: Polarized vector spiraling elliptic solitons in nonlocal nonlinear media. Opt. Commun. 352, 39–44 (2015)

  30. Abramowitz, M., Stegun, I.: Hand book of Mathematical Functions. Dover, NewYork (1965)

    Google Scholar 

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

    Article  Google Scholar 

  32. Dai, C.Q., Wang, Y.Y., Wang, X.G.: Ultrashort self-similar solutions of the cubic-quintic nonlinear Schrodinger equation with distributed coefficients in the inhomogeneous fiber. J. Phys. A Math. Theor. 44, 155203 (2011)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 11375079).

Author information

Authors and Affiliations

  1. College of Medicine and Health, Zhejiang Lishui University, Lishui, 323000, Zhejiang, China

    Hai-Yan Chen

  2. College of Ecology, Lishui University, Lishui, 323000, Zhejiang, China

    Hai-Ping Zhu

Authors
  1. Hai-Yan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hai-Ping Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hai-Ping Zhu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, HY., Zhu, HP. Self-similar azimuthons in strongly nonlocal nonlinear media with \({\varvec{{\mathcal {PT}}}}\)-symmetry. Nonlinear Dyn 84, 2017–2023 (2016). https://doi.org/10.1007/s11071-016-2625-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-016-2625-4

Keywords

Search

Navigation