Advertisement

Excitation management of (2+1)-dimensional breathers for a coupled partially nonlocal nonlinear Schrödinger equation with variable coefficients

  • Hong-Yu WuEmail author
  • Li-Hong Jiang
Original Paper
  • 53 Downloads

Abstract

The Akhmediev-breather and Ma-breather solutions of a (2+1)-dimensional variable-coefficient coupled partially nonlocal nonlinear Schrödinger equation with non-localized in y-direction nonlinearities and localized in x and z directions are constructed. From these solutions, the excitation management of (2+1)-dimensional breathers including the complete excitation, rear excitation, peak excitation and initial excitation is studied via the comparison of values between the maximum value of effective propagation distance and the location of peak in breathers.

Keywords

Excitation management (2+1)-Dimensional breathers Partially nonlocal nonlinearity (2+1)-Dimensional nonlinear Schrödinger equation Variable coefficients 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11775104).

Compliances with ethical standards

Conflict of interest

The authors have declared that no conflict of interest exists.

References

  1. 1.
    Zhang, Y., Dong, H., Zhang, X., Yang, H.: Rational solutions and lump solutions to the generalized (3 + 1)-dimensional shallow water-like equation. Comput. Math. Appl. 73, 246–252 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Guo, M., Fu, C., Zhang, Y., Liu, J., Yang, H.: Study of Ion-Acoustic solitary waves in a magnetized plasma using the three-dimensional time-space fractional Schamel–KdV equation. Complexity, 2018. UNSP 6852548 (2018).  https://doi.org/10.1155/2018/6852548
  3. 3.
    Zhang, X.E., Chen, Y., Zhang, Y.: Breather, lump and X soliton solutions to nonlocal KP equation. Comput. Math. Appl. 74, 2341–2347 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Ding, D.J., Jin, D.Q., Dai, C.Q.: Analytical solutions of differential-difference sine-Gordon equation. Therm Sci 21, 1701–1705 (2017)CrossRefGoogle Scholar
  5. 5.
    Chen, J.C., Ma, Z.Y., Hu, Y.H.: Nonlocal symmetry, nonlocal symmetry, Darboux transformation and soliton–cnoidal wave interaction solution for the shallow water wave equation. J. Math. Anal. Appl. 460, 987–1003 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Tao, M., Zhang, N., Gao, D., Yang, H.: Symmetry analysis for three-dimensional dissipation Rossby waves. Adv. Differ. Equ. 2018, 300 (2018).  https://doi.org/10.1186/s13662-018-1768-7 MathSciNetCrossRefGoogle Scholar
  7. 7.
    Ma, Z.Y., Chen, J.C., Fei, J.X.: Lump and line soliton pairs to a (2+1)-dimensional integrable Kadomtsev–Petviashvili equation. Comput. Math. Appl. 76, 1130–1138 (2018)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ma, W.X., Yong, X.L., Zhang, H.Q.: Diversity of interaction solutions to the (2+1)-dimensional Ito equation. Comput. Math. Appl. 75, 289–295 (2018)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Zhu, S.D., Song, J.F.: Residual symmetries, nth Bäcklund transformation and interaction solutions for (2+1)-dimensional generalized Broer–Kaup equations. Appl. Math. Lett. 83, 33–39 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Zhang, N., Xia, T., Jin, Q.: N-fold Darboux transformation of the discrete Ragnisco–Tu system. Adv. Differ. Equ. 2018, 302 (2018).  https://doi.org/10.1186/s13662-018-1751-3 MathSciNetCrossRefGoogle Scholar
  11. 11.
    Serkin, V.N., Hasegawa, A.: Exactly integrable nonlinear Schrodinger equation models with varying dispersion, nonlinearity and gain: application for soliton dispersion management. IEEE J. Sel. Top. Quantum Electron. 8, 418–431 (2002)CrossRefGoogle Scholar
  12. 12.
    Fu, C., Lu, C., Yang, H.W.: Time-space fractional (2+1) dimensional nonlinear Schrödinger equation for envelope gravity waves in baroclinic atmosphere and conservation laws as well as exact solutions. Adv. Differ. Equ. 2018, 56 (2018).  https://doi.org/10.1186/s13662-018-1512-3 CrossRefzbMATHGoogle Scholar
  13. 13.
    Zhang, Y., Yang, C., Yu, W., Liu, M., Ma, G., Liu, W.: Some types of dark soliton interactions in inhomogeneous optical fibers. Opt. Quantum Electron. 50, 295 (2018). Please check and confirm the article title is correctly identified for the reference [13]CrossRefGoogle Scholar
  14. 14.
    Liu, W., Liu, M., Han, H., Fang, S., Teng, H., Lei, M., Wei, Z.: Nonlinear optical properties of WSe2 and MoSe2 films and their applications in passively Q-switched erbium doped fiber lasers. Photonics Res. 6, C15–C21 (2018)CrossRefGoogle Scholar
  15. 15.
    Liu, W., Liu, M., OuYang, Y., Hou, H., Lei, M., Wei, Z.: CVD-grown MoSe2 with high modulation depth for ultrafast mode-locked erbium-doped fiber laser. Nanotechnology 29, 394002 (2018)CrossRefGoogle Scholar
  16. 16.
    Wang, Y.Y., Chen, L., Dai, C.Q., Zheng, J., Fan, Y.: Exact vector multipole and vortex solitons in the media with spatially modulated cubic-quintic nonlinearity. Nonlinear Dyn. 90, 1269–1275 (2017)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Wang, Y.Y., Dai, C.Q., Xu, Y.Q., Zheng, J., Fan, Y.: Dynamics of nonlocal and localized spatiotemporal solitons for a partially nonlocal nonlinear Schrodinger equation. Nonlinear Dyn. 92, 1261–1269 (2018)CrossRefGoogle Scholar
  18. 18.
    Dai, C.Q., Zhou, G.Q., Chen, R.P., Lai, X.J., Zheng, J.: Vector multipole and vortex solitons in two-dimensional Kerr media. Nonlinear Dyn. 88, 2629–2635 (2017)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Liu, W., Liu, M., Yin, J., Chen, H., Lu, W., Fang, S., Teng, H., Lei, M., Yan, P., Wei, Z.: Tungsten diselenide for all-fiber lasers with the chemical vapor deposition method. Nanoscale 10, 7971–7977 (2018)CrossRefGoogle Scholar
  20. 20.
    Liu, M., Liu, W., Yan, P., Fang, S., Teng, H., Wei, Z.: High-power MoTe2-based passively Q-switched erbium-doped fiber laser. Chin. Opt. Lett. 16, 020007 (2018)CrossRefGoogle Scholar
  21. 21.
    Ma, Y.C.: The perturbed plane-wave solution of the cubic Schrodinger equation. Stud. Appl. Math. 60, 43–58 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Akhmediev, N., Korneev, V.I.: Modulation instability and periodic solutions of the nonlinear Schrodinger equation. Theor. Math. Phys. 69, 1089–1093 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Kedziora, D.J., Ankiewicz, A., Akhmediev, N.: Circular rogue wave clusters. Phys. Rev. E 84, 056611 (2011)CrossRefzbMATHGoogle Scholar
  24. 24.
    Osborne, A.R.: Nonlinear Ocean Waves and the Inverse Scattering Transform. Elsevier, Amsterdam (2010)zbMATHGoogle Scholar
  25. 25.
    Kedziora, D.J., Ankiewicz, A., Akhmediev, N.: Second-order nonlinear Schrodinger equation breather solutions in the degenerate and rogue wave limits. Phys. Rev. E 85, 066601 (2012)CrossRefGoogle Scholar
  26. 26.
    Dai, C.Q., Huang, W.H.: Multi-rogue wave and multi-breather solutions in PT-symmetric coupled waveguides. Appl. Math. Lett. 32, 35–40 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Li, J.T., Zhang, X.T., Meng, M., Liu, Q.T., Wang, Y.Y., Dai, C.Q.: Control and management of the combined Peregrine soliton and Akhmediev breathers in PT-symmetric coupled waveguides. Nonlinear Dyn. 84, 473–479 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    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)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Królikowski, 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. J. Opt. B 6, S288 (2004)CrossRefGoogle Scholar
  30. 30.
    Zhong, W.P., Xie, R.H., Belic, M., Petrovic, N., Chen, G., Yi, L.: Exact spatial soliton solutions of the two-dimensional generalized nonlinear Schrodinger equation with distributed coefficients. Phys. Rev. A 78, 023821 (2008)CrossRefGoogle Scholar
  31. 31.
    Chen, H.Y., Zhu, H.P.: Self-similar azimuthons in strongly nonlocal nonlinear media with PT-symmetry. Nonlinear Dyn. 84, 2017–2023 (2016)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Wu, H.Y., Jiang, L.H.: Vector Hermite–Gaussian spatial solitons in (2+1)-dimensional strongly nonlocal nonlinear media. Nonlinear Dyn. 83, 713–718 (2016)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Dai, C.Q., Fan, Y., Zhou, G.Q., Zheng, J., Chen, L.: Vector spatiotemporal localized structures in (3 + 1)-dimensional strongly nonlocal nonlinear media. Nonlinear Dyn. 86, 999–1005 (2016)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Dai, C.Q., Wang, Y.Y.: Spatiotemporal localizations in (3 + 1)-dimensional PT-symmetric and strongly nonlocal nonlinear media. Nonlinear Dyn. 83, 2453–2459 (2016)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Yang, J.: Physically significant nonlocal nonlinear Schrödinger equation and its soliton solutions. Phys. Rev. E 98, 042202 (2018)CrossRefGoogle Scholar
  36. 36.
    Wang, Y.Y., Dai, C.Q., Xu, Y.Q., Zheng, J., Fan, Y.: Dynamics of nonlocal and localized spatiotemporal solitons for a partially nonlocal nonlinear Schrodinger equation. Nonlinear Dyn. 92, 1261–1269 (2018)CrossRefGoogle Scholar
  37. 37.
    Dai, C.Q., Wang, Y., Liu, J.: Spatiotemporal Hermite–Gaussian solitons of a (3 + 1)-dimensional partially nonlocal nonlinear Schrodinger equation. Nonlinear Dyn. 84, 1157–1161 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Yan, Z.Y.: Rogon-like solutions excited in the two-dimensional nonlocal nonlinear Schrödinger equation. J. Math. Anal. Appl. 380, 689–696 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    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. 88, 1373–1383 (2017)CrossRefGoogle Scholar
  40. 40.
    Dai, C.Q., Zhu, S.Q., Wang, L.L., Zhang, J.F.: Exact spatial similaritons for the generalized (2+1)-dimensional nonlinear Schrodinger equation with distributed coefficients. Europhys. Lett. 92, 24005 (2010)CrossRefGoogle Scholar
  41. 41.
    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
  42. 42.
    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)CrossRefGoogle Scholar
  43. 43.
    Reeves-Hall, P.C., Taylor, J.R.: Wavelength and duration tunable sub-picosecond source using adiabatic Raman compression. Electron. Lett. 37, 417–418 (2001)CrossRefGoogle Scholar
  44. 44.
    Reeves-Hall, P.C., Lewis, S.A.E., Chernikov, S.V., Taylor, J.R.: Picosecond soliton pulse-duration-selectable source based on adiabatic compression in Raman amplifier. Electron. Lett. 36, 622–624 (2000)CrossRefGoogle Scholar
  45. 45.
    Serkin, V.N., Hasegawa, A., Belyaeva, T.L.: Nonautonomous solitons in external potentials. Phys. Rev. Lett. 98, 074102 (2007)CrossRefGoogle Scholar
  46. 46.
    Serkin, V.N., Hasegawa, A.: Novel soliton solutions of the nonlinear Schrodinger equation model. Phys. Rev. Lett. 85, 4502–4505 (2000)CrossRefGoogle Scholar
  47. 47.
    Dai, C.Q., Wang, Y.Y., Zhang, J.F.: Analytical spatiotemporal localizations for the generalized (3+1)-dimensional nonlinear Schrodinger equation. Opt. Lett. 35, 1437–1439 (2010)CrossRefGoogle Scholar
  48. 48.
    Dai, C.Q., Wang, X.G.: Light bullet in parity-time symmetric potential. Nonlinear Dyn. 77, 1133–1139 (2014)MathSciNetCrossRefGoogle Scholar
  49. 49.
    Kruglov, V.I., Peacock, A.C., Harvey, J.D.: Exact self-similar solutions of the generalized nonlinear Schrodinger equation with distributed coefficients. Phys. Rev. Lett. 90, 113902 (2003)CrossRefGoogle Scholar
  50. 50.
    Yang, R., Hao, R., Li, L., Shi, X., Li, Z., Zhou, G.: Exact gray multi-soliton solutions for nonlinear Schrodinger equation with variable coefficients. Opt. Commun. 253, 177–185 (2005)CrossRefGoogle Scholar
  51. 51.
    Wang, J., Li, L., Jia, S.: Exact chirped gray soliton solutions of the nonlinear Schrodinger equation with variable coefficients. Opt. Commun. 274, 223–230 (2007)CrossRefGoogle Scholar
  52. 52.
    Dai, C.Q., Wang, Y.Y., Zhang, J.F.: Nonlinear similariton tunneling effect in the birefringent fiber. Opt. Express 18, 17548–17554 (2010)CrossRefGoogle Scholar
  53. 53.
    Dai, C.Q., Zhang, J.F.: Exact spatial similaritons and rogons in 2D graded-index waveguides. Opt. Lett. 35, 2651–2653 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.College of Engineering and DesignLishui UniversityLishuiChina

Personalised recommendations