Skip to main content
SpringerLink
Log in

A general nonlocal nonlinear Schrödinger equation with shifted parity, charge-conjugate and delayed time reversal

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

Abstract

A general nonlocal nonlinear Schrödinger equation with shifted parity, charge-conjugate and delayed time reversal is derived from the nonlinear inviscid dissipative and equivalent barotropic vorticity equation in a \(\beta \)-plane. The modulational instability (MI) of the obtained system is studied, which reveals a number of possibilities for the MI regions due to the generalized dispersion relation that relates the frequency and wavenumber of the modulating perturbations. Exact periodic solutions in terms of Jacobi elliptic functions are obtained, which, in the limit of the modulus approaches unity, reduce to soliton, kink solutions and their linear superpositions. Representative profiles of different nonlinear wave excitations are displayed graphically. These solutions can be used to model different blocking events in climate disasters. As an illustration, a special approximate solution is given to describe a kind of two correlated dipole blocking events.

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
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Ablowitz, M.J., Musslimani, Z.H.: Integrable nonlocal nonlinear Schrödinger equation. Phys. Rev. Lett. 110, 064105 (2013)

    Article  Google Scholar 

  2. Pertsch, T., Peschel, U., Kobelke, J., Schuster, K., Bartelt, H., Nolte, S., Tunnermann, A., Lederer, F.: Nonlinearity and disorder in fiber arrays. Phys. Rev. Lett. 93, 053901 (2004)

    Article  Google Scholar 

  3. Ablowitz, M.J., Musslimani, Z.H.: Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation. Nonlinearity 29, 915–946 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fokas, A.S.: Integrable multidimensional versions of the nonlocal nonlinear Schrödinger equation. Nonlinearity 29, 319–324 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  5. Liu, Y.B., Mihalache, D., He, J.S.: Families of rational solutions of the y-nonlocal Davey–Stewartson II equation. Nonlinear Dyn. 90(4), 2445–2455 (2017)

    Article  MathSciNet  Google Scholar 

  6. Liu, Y.K., Li, B.: Rogue waves in the (\(2+1\))-dimensional nonlinear Schrödinger equation with a parity-time-symmetric potential. Chin. Phys. Lett. 34, 010202 (2017)

    Article  Google Scholar 

  7. Ablowitz, M.J., Musslimani, Z.H.: Integrable discrete PT symmetric model. Phys. Rev. E 90, 032912 (2014)

    Article  Google Scholar 

  8. Ma, L.Y., Zhu, Z.N.: N-soliton solution for an integrable nonlocal discrete focusing nonlinear Schrödinger equation. Appl. Math. Lett. 59, 115–121 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhang, Y., Liu, Y.P., Tang, X.Y.: A general integrable three-component coupled nonlocal nonlinear Schrodinger equation. Nonlinear Dyn. 89(4), 2729–2738 (2017)

    Article  MathSciNet  Google Scholar 

  10. Lou, S.Y., Huang, F.: Alice–Bob physics: coherent solutions of nonlocal KdV systems. Sci. Rep. 7, 869 (2017)

    Article  Google Scholar 

  11. Tang, X.Y., Zhao, J., Huang, F., Lou, S.Y.: Monopole blocking governed by a modified KdV type equation. Stud. Appl. Math. 122, 295–304 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ablowitz, M.J., Musslimani, Z.H.: Integrable nonlocal nonlinear equations. Stud. Appl. Math. 139, 7–59 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. Jia, M., Gao, Y., Huang, F., Lou, S.Y., Sun, J.L., Tang, X.Y.: Vortices and vortex sources of multiple vortex interaction systems. Nonlinear Anal. Real Word Appl. 13, 2079 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  14. Dudley, J.M., Genty, G., Dias, F., Kibler, B., Akhmediev, N.: Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation. Opt. Express 23, 21497 (2009)

    Article  Google Scholar 

  15. Solli, D.R., Ropers, C., Koonath, P., Jalali, B.: Optical rogue waves. Nature 450, 1054–1057 (2007)

    Article  Google Scholar 

  16. Khare, A., Saxena, A.: Periodic and hyperbolic soliton solutions of a number of nonlocal nonlinear equations. J. Math. Phys. 56, 032104 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  17. Luo, D.H., Li, J.P.: Interaction between a slowly moving planetary-scale dipole envelop Rossby soliton and a wavenumber-two topography in a forced higher order nonlinear Schrödinger equation. Adv. Atmos. Sci. 19, 239–256 (2001)

    Google Scholar 

Download references

Acknowledgements

The authors acknowledge the financial support by the National Natural Science Foundation of China (Nos. 11675055 and 11475052) and Shanghai Knowledge Service Platform for Trustworthy Internet of Things (No. ZF1213).

Author information

Authors and Affiliations

  1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China

    Xiao-Yan Tang

  2. Department of Physics, Hangzhou Normal University, Hangzhou, 310036, China

    Zu-Feng Liang

Authors
  1. Xiao-Yan Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zu-Feng Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiao-Yan Tang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tang, XY., Liang, ZF. A general nonlocal nonlinear Schrödinger equation with shifted parity, charge-conjugate and delayed time reversal. Nonlinear Dyn 92, 815–825 (2018). https://doi.org/10.1007/s11071-018-4092-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-018-4092-6

Keywords

Search

Navigation