Skip to main content
SpringerLink
Log in

Scalar and vector multipole and vortex solitons in the spatially modulated cubic–quintic nonlinear media

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

Abstract

We derive scalar and vector multipole and vortex soliton solutions in the spatially modulated cubic–quintic nonlinear media, which is governed by a (3+1)-dimensional N-coupled cubic–quintic nonlinear Schrödinger equation with spatially modulated nonlinearity and transverse modulation. If the modulation depth \(q=1\), the vortex soliton is constructed, and if \(q=0\), the multipole soliton, including dipole, quadrupole, hexapole, octopole and dodecagon solitons, is constructed, respectively, when the topological charge \(k=1\)–5. If the topological charge \(k=0\), scalar solitons can be obtained. Moreover, the number of layers for the scalar and vector multipole and vortex solitons is decided by the value of the soliton order number n.

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
Fig. 4

Similar content being viewed by others

References

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

    Article  Google Scholar 

  2. Biswas, A., Mirzazadeh, M., Eslami, M., Milovic, D., Belic, M.: Solitons in optical metamaterials by functional variable method and first integral approach. Frequenz 68(11–12), 525–530 (2014)

    Google Scholar 

  3. Kong, L.Q., Dai, C.Q.: Some discussions about variable separation of nonlinear models using Riccati equation expansion method. Nonlinear Dyn. 81, 1553–1561 (2015)

    Article  MathSciNet  Google Scholar 

  4. 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)

    Article  MATH  Google Scholar 

  5. 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)

    Article  MathSciNet  Google Scholar 

  6. Wang, Y.Y., Dai, C.Q., Zhou, G.Q., Fan, Y., Chen, L.: Rogue wave and combined breather with repeatedly excited behaviors in the dispersion/diffraction decreasing medium. Nonlinear Dyn. 87, 67–73 (2017)

    Article  Google Scholar 

  7. Stegeman, G.I., Segev, M.: Optical spatial solitons and their interactions: universality and diversity. Science 286, 1518–1523 (1999)

    Article  Google Scholar 

  8. Dai, C.Q., Wang, X.G.: Light bullet in parity-time symmetric potential. Nonlinear Dyn. 77, 1133–1139 (2014)

    Article  MathSciNet  Google Scholar 

  9. 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)

    Article  Google Scholar 

  10. Li, J.T., Zhu, Y., Liu, Q.T., Han, J.Z., Wang, Y.Y., Dai, C.Q.: Vector combined and crossing Kuznetsov-Ma solitons in PT-symmetric coupled waveguides. Nonlinear Dyn. 85, 973–980 (2016)

    Article  MathSciNet  Google Scholar 

  11. 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). https://doi.org/10.1007/s11071-016-3316-x

    Google Scholar 

  12. Xu, Y.J.: Hollow ring-like soliton and dipole soliton in (2+ 1)-dimensional PT-symmetric nonlinear couplers with gain a nd loss. Nonlinear Dyn. 83, 1497–1501 (2016)

    Article  Google Scholar 

  13. Wu, H.Y., Jiang, L.H.: Vector Hermite-Gaussian spatial solitons in (2+1)-dimensional stro ngly nonlocal nonlinear media. Nonlinear Dyn. 83, 713–718 (2016)

    Article  Google Scholar 

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

    Article  Google Scholar 

  15. Zhu, H.P., Chen, L., Chen, H.Y.: Hermite-Gaussian vortex solitons of a (3+1)-dimensional partially nonlocal nonlinear Schrodinger equation with variable coefficients. Nonlinear Dyn. 85, 1913–1918 (2016)

    Article  MathSciNet  Google Scholar 

  16. Pusharov, D.I., Tanev, S.: Bright and dark solitary wave propagation and bistability in the anomalous dispersion region of optical waveguides with third- and fifth-order nonlinearities. Opt. Commun. 124, 354–364 (1996)

    Article  Google Scholar 

  17. Abdullaev, F.K., Salerno, M.: Gap-Townes solitons and localized excitations in low-dimensional Bose–Einstein condensates in optical lattices. Phys. Rev. A 72, 033617 (2005)

    Article  Google Scholar 

  18. Dai, C.Q., Wang, Y.: Higher-dimensional localized mode families in parity-time-symmetric potentials with competing nonlinearities. J. Opt. Soc. Am. B 31, 2286–2294 (2014)

    Article  Google Scholar 

  19. 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  Google Scholar 

  20. Mani Rajan, M.S.: Unexpected behavior on nonlinear tunneling of chirped ultrashort soliton pulse in non-Kerr media with Raman effect. Z. Naturforsch. A 71, 751–758 (2016)

  21. Serkin, V.N., Belyaeva, T.L., Alexandrov, I.V., Melchor, G.M.: Novel topological quasi-soliton solutions for the nonlinear cubic–quintic Schrodinger equation model. In: Proceedings of SPIE-The International Society for Optical Engineering 4271, pp. 292–302 (2001)

  22. Dai, C.Q., Wang, D.S., Wang, L.L.: Quasi-two-dimensional Bose–Einstein condensates with spatially modulated cubic–quintic nonlinearities. Ann. Phys. 326, 2356–2368 (2011)

  23. Dai, C.Q., Chen, R.P., Wang, Y.Y.: Spatiotemporal self-similar solutions for the nonautonomous (3+1)-dimensional cubic–quintic Gross–Pitaevskii equation. Chin. Phys. B 21, 030508 (2012)

    Article  Google Scholar 

  24. Belmonte-Beitia, J., Cuevas, J.: Solitons for the cubic–quintic nonlinear Schrodinger equation with time- and space-modulated coefficients. J. Phys. A Math. Theor. 42, 165201 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Avelar, A.T., Bazeia, D., Cardoso, W.B.: Solitons with cubic and quintic nonlinearities modulated in space and time. Phys. Rev. E 79, 025602 (2009)

    Article  Google Scholar 

  26. Song, X., Li, H.M.: Stable vortex solitons of (2 + 1)-dimensional cubic–quintic Gross–Pitaevskii equation with spatially inhomogeneous nonlinearities. Phys. Lett. A 377, 714–717 (2013)

    Article  MathSciNet  Google Scholar 

  27. Mani Rajan, M.S., Hakkim, J., Mahalingam, A., Uthayakumar, A.: Dispersion management and cascade compression of femtosecond nonautonomous soliton in birefringent fiber. Eur. Phys. J. D 67, 150–157 (2013)

    Article  Google Scholar 

  28. Mani Rajan, M.S., Mahalingam, A., Uthayakumar, A.: Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation. Ann. Phys. 346, 1–13 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  29. Agrawal, G.P.: Nonlinear Fiber Optics. Academic Press, New York (1995)

    MATH  Google Scholar 

  30. Gomez-Alcala, R., Dengra, A.: Vector soliton switching by using the cascade connection of saturable absorbers. Opt. Lett. 31, 3137–3139 (2006)

    Article  Google Scholar 

  31. Manakov, S.V.: On the theory of two-dimensional stationary self-focusing of electromagnetic waves. Sov. Phys.-JETP 38, 248–253 (1974)

    MathSciNet  Google Scholar 

  32. Radhakrishnan, R., Aravinthan, K.: A dark-bright optical soliton solution to the coupled nonlinear Schrödinger equation. J. Phys. A Math. Theor. 40, 13023 (2007)

    Article  MATH  Google Scholar 

  33. 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)

    Article  Google Scholar 

  34. Kong, L.Q., Liu, J., Jin, D.Q., Ding, D.J., Dai, C.Q.: Soliton dynamics in the three-spine \(\alpha \)-helical protein with inhomogeneous effect. Nonlinear Dyn. 87, 83–92 (2017)

  35. Mahalingam, A., Mani Rajan, M.S.: Influence of generalized external potentials on nonlinear tunneling of nonautonomous solitons: soliton management. Opt. Fiber Technol. 25, 44–50 (2015)

    Article  Google Scholar 

  36. Mani Rajan, M.S., Mahalingam, A.: Multi-soliton propagation in a generalized inhomogeneous nonlinear Schrodinger–Maxwell-Bloch system with loss/gain. J. Math. Phys. 54, 043514 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  37. Belmonte-Beitia, J., Perez-Garcia, V.M., Vekslerchik, V., Torres, P.J.: Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities. Phys. Rev. Lett. 98, 064102 (2007)

    Article  Google Scholar 

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

    MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (11781240085 and 11747148), the Program for Science & Technology Innovation Talents in Universities of Henan Province (18HASTIT032), and the High-level Talents Research and Startup Foundation Projects for Doctors of Zhoukou Normal University (zknu2014120).

Author information

Authors and Affiliations

  1. School of Physics and Telecommunications Engineering, Zhoukou Normal University, Zhoukou, 466001, People’s Republic of China

    Ji-tao Li, Yu Zhu, Jin-zhong Han, Wei Qin & Shao-hui Wang

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

    Chao-qing Dai

Authors
  1. Ji-tao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jin-zhong Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wei Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Chao-qing Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Shao-hui Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yu Zhu or Jin-zhong Han.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Jt., Zhu, Y., Han, Jz. et al. Scalar and vector multipole and vortex solitons in the spatially modulated cubic–quintic nonlinear media. Nonlinear Dyn 91, 757–765 (2018). https://doi.org/10.1007/s11071-017-3744-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-017-3744-2

Keywords

Search

Navigation