Advertisement

Nonlinear Dynamics

, Volume 88, Issue 4, pp 2629–2635 | Cite as

Vector multipole and vortex solitons in two-dimensional Kerr media

  • Chao-Qing Dai
  • Guo-Quan Zhou
  • Rui-Pin Chen
  • Xian-Jing Lai
  • Jun Zheng
Original Paper

Abstract

We investigate a (2+1)-dimensional coupled nonlinear Schrödinger equation with spatially modulated nonlinearity and transverse modulation, and derive analytical vector multipole and vortex soliton solution. When the modulation depth q is chosen as 0 and 1, vector multipole and vortex solitons are constructed, respectively. The number of azimuthal lobes (“petals”) for the multipole solitons is determined by the value of 2m with the topological charge m, and the number of layers in the multipole solitons is determined by the value of the soliton order number n.

Keywords

Vector multipole soliton Vector vortex soliton (2+1)-dimensional coupled nonlinear schrödinger equation Kerr nonlinear media 

Notes

Acknowledgements

This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant Nos. LY17F050011, LY16A040014 and LQ16A040003), and National Natural Science Foundation of China (Grant Nos. 11375007, 11574272 and 11574271). 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.

References

  1. 1.
    Zhou, Q., Mirzazadeh, M., Ekici, M., Sonmezoglu, A.: Optical solitons in media with time-modulated nonlinearities and spatiotemporal dispersion. Nonlinear Dyn. 86, 623–638 (2016)CrossRefzbMATHGoogle Scholar
  2. 2.
    Zhou, Q.: Optical solitons for Biswas–Milovic model with Kerr law and parabolic law nonlinearities. Nonlinear Dyn. 84, 677–681 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Liu, W.J., Pang, L.H., Han, H.N., Tian, W.L., Chen, H., Lei, M., Yan, P.G., Wei, Z.Y.: 70-fs mode-locked erbium-doped fiber laser with topological insulator. Sci. Rep. 6, 19997 (2016)CrossRefGoogle Scholar
  4. 4.
    Zhou, Q., Ekici, M., Sonmezoglu, A., Mirzazadeh, M., Eslami, M.: Optical solitons with Biswas–Milovic equation by extended trial equation method. Nonlinear Dyn. 84, 1883–1900 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Stegeman, G.I., Segev, M.: Optical spatial solitons and their interactions: Universality and diversity. Science 286, 1518–1523 (1999)CrossRefGoogle Scholar
  6. 6.
    Dai, C.Q., Chen, R.P., Wang, Y.Y., Fan, Y.: Dynamics of light bullets in inhomogeneous cubic-quintic-septimal nonlinear media with PT-symmetric potentials. Nonlinear Dyn. 87, 1675–1683 (2017)CrossRefGoogle Scholar
  7. 7.
    Kivshar, Y.S., Agrawal, G.P.: Optical Solitons: From Fibers to Photonic Crystals. Academic, San Diego (2003)Google Scholar
  8. 8.
    Xu, S.L., Xue, L., Belic, M.R., He, J.R.: Spatiotemporal soliton clusters in strongly nonlocal media with variable potential coefficients. Nonlinear Dyn. 87, 1856–1864 (2016)MathSciNetGoogle Scholar
  9. 9.
    Zhang, B., Zhang, X.L., Dai., C.Q.: Discussions on localized structures based on equivalent solution with different forms of breaking soliton model. Nonlinear Dyn. (2016). doi: 10.1007/s11071-016-3197-z
  10. 10.
    Dai, C.Q., Liu, J., Fan, Y., Yu, D.G.: Two-dimensional localized Peregrine solution and breather excited in a variable-coefficient nonlinear Schrödinger equation with partial nonlocality. Nonlinear Dyn. (2017). doi: 10.1007/s11071-016-3316-x
  11. 11.
    Dai, C.Q., Fan, Y., Zhou, G.Q., Zheng, J., Cheng, L.: Vector spatiotemporal localized structures in (3+1)-dimensional strongly nonlocal nonlinear media. Nonlinear Dyn. 86, 999–1005 (2016)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Desyatnikov, A.S., Sukhorukov, A.A., Kivshar, Y.S.: Azimuthons: spatially modulated vortex solitons. Phys. Rev. Lett. 95, 203904 (2005)CrossRefGoogle Scholar
  13. 13.
    Towers, I., Malomed, B.A.: Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity”. J. Opt. Soc. Am. B 19, 537 (2002)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Wu, L., Li, L., Zhang, J.F., Mihalache, D., Malomed, B.A., Liu, W.M.: Exact solutions of the Gross–Pitaevskii equation for stable vortex modes in two-dimensional Bose–Einstein condensates. Phys. Rev. A 81, 061805(R) (2010)CrossRefGoogle Scholar
  15. 15.
    Quiroga-Teixeiro, M., Michinel, H.: Stable azimuthal stationary state in quintic nonlinear optical media. J. Opt. Soc. Am. B 14, 2004–2009 (1997)CrossRefGoogle Scholar
  16. 16.
    Zhong, W.P., Belic, M.R., Huang, T.W.: Two-dimensional accessible solitons in PT-symmetric potentials. Nonlinear Dyn. 70, 2027–2034 (2012)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Radhakrishnan, R., Aravinthan, K.: A dark-bright optical soliton solution to the coupled nonlinear Schrödinger equation”. J. Phys. A Math. Theor. 40, 13023 (2007)CrossRefzbMATHGoogle Scholar
  18. 18.
    Sun, Z.Y., Gao, Y.T., Yu, X., Liu, W.J., Liu, Y.: Bound vector solitons and soliton complexes for the coupled nonlinear Schrödinger equations. Phys. Rev. E 80, 066608 (2009)CrossRefGoogle Scholar
  19. 19.
    Manakov, S.V.: On the theory of two-dimensional stationary self-focusing of electromagnetic waves. Sov. Phys. JETP 38, 248–253 (1974)MathSciNetGoogle Scholar
  20. 20.
    Zhong, W.P., Belic, M.R., Assanto, G., Malomed, B.A., Huang, T.W.: Self-trapping of scalar and vector dipole solitary waves in Kerr media. Phys. Rev. A 83, 043833 (2011)CrossRefGoogle Scholar
  21. 21.
    Agrawal, G.P.: Nonlinear Fiber Opt. Academic, New York (1995)Google Scholar
  22. 22.
    Gomez-Alcala, R., Dengra, A.: Vector soliton switching by using the cascade connection of saturable absorbers. Opt. Lett. 31, 3137–3139 (2006)CrossRefGoogle Scholar
  23. 23.
    Neshev, D.N., Alexander, T.J., Ostrovskaya, E.A., Kivshar, YuS, Martin, H., Makasyuk, I., Chen, Z.G.: Observation of discrete vortex solitons in optically induced photonic lattices. Phys. Rev. Lett. 92, 123903 (2004)CrossRefGoogle Scholar
  24. 24.
    Hao, R.Y., Zhou, G.S.: Propagation of light in (2+1)-dimensional nonlinear optical media with spatially inhomogeneous nonlinearities. Chin. Opt. Lett. 6, 211–213 (2008)CrossRefGoogle Scholar
  25. 25.
    Wang, Y., Hao, R.Y.: Exact spatial soliton solution for nonlinear Schrödinger equation with a type of transverse nonperiodic modulation. Opt. Commun. 282, 3995–3998 (2009)CrossRefGoogle Scholar
  26. 26.
    Heinrich, M., Kartashov, Y.V., Ramirez, L.P.R., Szameit, A., Dreisow, F., Keil, R., Nolte, S., Tünnermann, A., Vysloukh, V.A., Torner, L.: Observation of two-dimensional superlattice solitons. Opt. Lett. 34, 3701–3703 (2009)CrossRefGoogle Scholar
  27. 27.
    Belmonte-Beitia, J., Perez-Garcia, V.M., Vekslerchik, V., Konotop, V.V.: Localized nonlinear waves in systems with time-and space-modulated nonlinearities. Phys. Rev. Lett. 100, 164102 (2008)CrossRefGoogle Scholar
  28. 28.
    Whittaker, E.T., Watson, G.N.: A Course in Modern Analysis, 4th edn. Cambridge University Press, Cambridge (1990)zbMATHGoogle Scholar
  29. 29.
    Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1972)Google Scholar
  30. 30.
    Tian, Q., Wu, L., Zhang, Y.H., Zhang, J.F.: Vortex solitons in defocusing media with spatially inhomogeneous nonlinearity. Phys. Rev. E 85, 056603 (2012)Google Scholar
  31. 31.
    Tian, Q., Wu, L., Zhang, J.F., Malomed, B.A., Mihalache, D., Liu, W.M.: Exact soliton solutions and their stability control in the nonlinear Schrodinger equation with spatiotemporally modulated nonlinearity. Phys. Rev. E 83, 016602 (2011)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Chao-Qing Dai
    • 1
  • Guo-Quan Zhou
    • 1
  • Rui-Pin Chen
    • 2
  • Xian-Jing Lai
    • 3
  • Jun Zheng
    • 1
  1. 1.School of SciencesZhejiang A&F UniversityLin’anPeople’s Republic of China
  2. 2.Department of PhysicsZhejiang Sci-Tech UniversityHangzhouPeople’s Republic of China
  3. 3.Department of Basic ScienceZhejiang Shuren UniversityHangzhouPeople’s Republic of China

Personalised recommendations