Skip to main content
SpringerLink
Log in

Vortex and multipole soliton modes in the (2 + 1)-dimensional cubic-quintic-septimal nonlinear media with the spatially modulated distributions

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

A (2 + 1)-dimensional cubic-quintic-septimal nonlinear Schrödinger equation with the spatially modulated distributions is investigated. When it is linked to the stationary cubic-quintic-septimal nonlinear Schrödinger equation, constraint conditions exist connecting inhomogeneous cubic, quintic and septimal nonlinearities and the amplitude of soliton mode. Under these conditions, analytical vortex and multipole soliton mode solutions are derived. If the value of the modulation depth is set as 1 and 0, vortex and multipole soliton modes are formed respectively. If the value of the soliton order number n grows, the layer structures of vortex and multipole soliton modes are added and are determined by the value of n. The stability of multipole and vortex soliton modes is tested by direct simulations with initial white noise.

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

Similar content being viewed by others

References

  1. L.H. Wang, J.T. Li, S.F. Li, Q.T. Liu, Eur. Phys. J. Plus 131, 211 (2016)

    Article  ADS  Google Scholar 

  2. H.Y. Wu, L.H. Jiang, Eur. Phys. J. Plus 133, 124 (2018)

    Article  Google Scholar 

  3. D.J. Ding, D.Q. Jin, C.Q. Dai, Therm. Sci. 21, 1701 (2017)

    Article  Google Scholar 

  4. Y.Y. Wang, Y.P. Zhang, C.Q. Dai, Nonlinear Dyn. 83, 1331 (2016)

    Article  Google Scholar 

  5. C.Q. Dai, S.Q. Zhu, L.L. Wang, J.F. Zhang, EPL 92, 24005 (2010)

    Article  ADS  Google Scholar 

  6. Y.Y. Wang, C.Q. Dai, Y.Q. Xu, J. Zheng, Y. Fan, Nonlinear Dyn. 92, 1261 (2018)

    Article  Google Scholar 

  7. Y.Y. Wang, L. Chen, C.Q. Dai, J. Zheng, Y. Fan, Nonlinear Dyn. 90, 1269 (2017)

    Article  Google Scholar 

  8. J.T. Li, Y. Zhu, Q.T. Liu, J.Z. Han, Y.Y. Wang, C.Q. Dai, Nonlinear Dyn. 85, 973 (2016)

    Article  Google Scholar 

  9. C.Q. Dai, Y.Y. Wang, J.F. Zhang, Opt. Express 18, 17548 (2010)

    Article  ADS  Google Scholar 

  10. R.P. Chen, C.Q. Dai, Nonlinear Dyn. 90, 1563 (2017)

    Article  Google Scholar 

  11. C.Q. Dai, Y.Y. Wang, Y. Fan, D.G. Yu, Nonlinear Dyn. 92, 1351 (2018)

    Article  Google Scholar 

  12. Y. Zhu, W. Qin, J.T. Li, J.Z. Han, Y.Y. Wang, C.Q. Dai, Nonlinear Dyn. 88, 1883 (2017)

    Article  Google Scholar 

  13. Q. Tian, L. Wu , Y.H. Zhang, J.F. Zhang, Phys. Rev. E 85, 056603 (2012)

    Article  ADS  Google Scholar 

  14. K.J.H. Law, P.G. Kevrekidis, Laurette S. Tuckerman, Phys. Rev. Lett. 105, 160405 (2010)

    Article  ADS  Google Scholar 

  15. D.I. Pusharov, S. Tanev, Opt. Commun. 124, 354 (1996)

    Article  ADS  Google Scholar 

  16. A.S. Reyna, B.A. Malomed, C.B. de Araújo, Phys. Rev. A 92, 033810 (2015)

    Article  ADS  Google Scholar 

  17. A.S. Reyna, C.B. de Araújo, Opt. Express 22, 22456 (2014)

    Article  ADS  Google Scholar 

  18. H.Y. Wu, L.H. Jiang, Y.F. Wu, Nonlinear Dyn. 87, 1667 (2017)

    Article  Google Scholar 

  19. C.Q. Dai, R.P. Chen, Y.Y. Wang, Y. Fan, Nonlinear Dyn. 87, 1675 (2017)

    Article  Google Scholar 

  20. H.P. Zhu, Z.H. Pan, Nonlinear Dyn. 89, 1745 (2017)

    Article  Google Scholar 

  21. Y.X. Chen, F.Q. Xu, Y.L. Hu, Nonlinear Dyn. 90, 1115 (2017)

    Article  Google Scholar 

  22. L.Q. Kong, C.Q. Dai, Nonlinear Dyn. 81, 1553 (2015)

    Article  Google Scholar 

  23. Y.Y. Wang, Y.P. Zhang, C.Q. Dai, Nonlinear Dyn. 83, 1331 (2016)

    Article  Google Scholar 

  24. Y.Y. Wang, C.Q. Dai, Appl. Math. Model. 40, 3475 (2016)

    Article  MathSciNet  Google Scholar 

  25. W.P. Zhong, M. Belic, G. Assanto, B.A. Malomed, T. Huang, Phys. Rev. A 84, 043801 (2011)

    Article  ADS  Google Scholar 

  26. J. Belmonte-Beitia, V.M. Perez-Garcia, V. Vekslerchik, V.V. Konotop, Phys. Rev. Lett. 100, 164102 (2008)

    Article  ADS  Google Scholar 

  27. E.T. Whittaker, G.N. Watson, A Course in Modern Analysis, 4th edition (Cambridge University Press, Cambridge, 1990)

  28. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1972)

  29. L. Gagnon, P. Winternitz, J. Phys. A: Math. Gen. 21, 1493 (1988)

    Article  ADS  Google Scholar 

  30. S.L. Xu, N. Petrović, Milivoj R. Belić, Nonlinear Dyn. 80, 583 (2015)

    Article  Google Scholar 

  31. R. Killip, T. Oh, O. Pocovnicu, M. Visan, Arch. Ration. Mech. Anal. 225, 469 (2017)

    Article  MathSciNet  Google Scholar 

  32. C.Q. Dai, D.S. Wang, L.L. Wang, J.F. Zhang, W.M. Liu, Ann. Phys. 326, 2356 (2011)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electronics Information, Zhejiang University of Media and Communications, 310018, Hangzhou, China

    Yi-Xiang Chen

Authors
  1. Yi-Xiang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yi-Xiang Chen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, YX. Vortex and multipole soliton modes in the (2 + 1)-dimensional cubic-quintic-septimal nonlinear media with the spatially modulated distributions. Eur. Phys. J. Plus 133, 396 (2018). https://doi.org/10.1140/epjp/i2018-12198-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2018-12198-3

Search

Navigation