Skip to main content
SpringerLink
Log in

Versatile excitations of 3D partially nonlocal bright–bright Peregrine-quartets in a nonautonomous vector nonlinear Schrödinger equation under a parabolic potential

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

Abstract

This paper aims to study versatile excitations of (3+1)-dimensional partially nonlocal bright–bright Peregrine-quartets in a nonautonomous vector nonlinear Schrödinger equation with different values of diffraction in two transverse directions under a parabolic potential. By simplifying a nonautonomous vector nonlinear Schrödinger equation into an autonomous one with its analytical solutions derived from the nonrecursive Darboux method, analytical solutions of the nonautonomous vector equation are deduced. Versatile excitations of (3+1)-dimensional partially nonlocal bright–bright Peregrine-quartets are investigated in an exponential diffraction system by comparing two values of maximum accumulated time with the excited time for Peregrine-quartets. Moreover, the effects of the different values of diffractions in two transverse directions on the dynamics of Peregrine-quartets are analyzed. When the values of diffractions add, the shape of Peregrine-quartets will alter. These results will help deeply understand the partially nonlocal wave phenomena in the diverse branches of optical engineering, BEC and other disciplines.

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

Similar content being viewed by others

Data availibility

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

References

  1. Wazwaz, A.M., Hammad, M.A., El-Tantawy, S.A.: Bright and dark optical solitons for (3 + 1)-dimensional hyperbolic nonlinear Schrodinger equation using a variety of distinct schemes. Optik 270, 170043 (2022)

    Google Scholar 

  2. Zhang, R.F., Li, M.C.: Bilinear residual network method for solving the exactly explicit solutions of nonlinear evolution equations. Nonlinear Dyn. 108, 521–531 (2022)

    Google Scholar 

  3. Kaur, L., Wazwaz, A.M.: Optical soliton solutions of variable coefficient Biswas–Milovic (BM) model comprising Kerr law and damping effect. Optik 266, 169617 (2022)

    Google Scholar 

  4. Wang, R.R., Wang, Y.Y., Dai, C.Q.: Influence of higher-order nonlinear effects on optical solitons of the complex Swift-Hohenberg model in the mode-locked fiber laser. Opt. Laser Technol. 152, 108103 (2022)

    Google Scholar 

  5. Wang, B.H., Wang, Y.Y., Dai, C.Q., Chen, Y.X.: Dynamical characteristic of analytical fractional solitons for the space-time fractional Fokas–Lenells equation. Alex. Eng. J. 59, 4699–4707 (2020)

    Google Scholar 

  6. Wazwaz, A.M.: New (3+1)-dimensional Painleve integrable fifth-order equation with third-order temporal dispersion. Nonlinear Dyn. 106, 891–897 (2021)

    Google Scholar 

  7. Zhang, R.F., Li, M.C., Gan, J., Li, Q., Lan, Z.Z.: Novel trial functions and rogue waves of generalized breaking soliton equation via bilinear neural network method. Chaos Solitons Fractals 154, 111692 (2022)

    MathSciNet  MATH  Google Scholar 

  8. Fang, Y., Wu, G.Z., Wang, Y.Y., Dai, C.Q.: Data-driven femtosecond optical soliton excitations and parameters discovery of the high-order NLSE using the PINN. Nonlinear Dyn. 105, 603–616 (2021)

    Google Scholar 

  9. Zhang, R.F., Bilige, S.: Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation. Nonlinear Dyn. 95, 3041–3048 (2019)

    MATH  Google Scholar 

  10. Wazwaz, A.M., Albalawi, W., El-Tantawy, S.A.: Optical envelope soliton solutions for coupled nonlinear Schrodinger equations applicable to high birefringence fibers. Optik 255, 168673 (2022)

    Google Scholar 

  11. Singla, S., Saini, N.S.: Dust acoustic kinetic Alfven wave solitons and periodic waves in a polarized dusty plasma. Euro. Phys. J Plus 137, 1111 (2022)

    Google Scholar 

  12. 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)

    MathSciNet  Google Scholar 

  13. Bo, W.B., Wang, R.R., Fang, Y., Wang, Y.Y., Dai, C.Q.: Prediction and dynamical evolution of multipole soliton families in fractional Schrodinger equation with the PT-symmetric potential and saturable nonlinearity. Nonlinear Dyn. 111, 1577–1588 (2023)

    Google Scholar 

  14. Ding, C.C., Zhou, Q., Triki, H., Sun, Y.Z., Biswas, A.: Dynamics of dark and anti-dark solitons for the x-nonlocal Davey–Stewartson II equation. Nonlinear Dyn. 111, 2621–2629 (2023)

    Google Scholar 

  15. Fang, Y., Wu, G.Z., Wen, X.K., Wang, Y.Y., Dai, C.Q.: Predicting certain vector optical solitons via the conservation-law deep-learning method. Opt. Laser Technol. 155, 108428 (2022)

    Google Scholar 

  16. Dai, C.Q., Wang, Y.Y.: Coupled spatial periodic waves and solitons in the photovoltaic photorefractive crystals. Nonlinear Dyn. 102, 1733–1741 (2020)

    Google Scholar 

  17. 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)

    Google Scholar 

  18. Zhou, Q., Xu, M.Y., Sun, Y.Z., Zhong, Y., Mirzazadeh, M.: Generation and transformation of dark solitons, anti-dark solitons and dark double-hump solitons. Nonlinear Dyn 110, 1747–1752 (2022)

    Google Scholar 

  19. Zhang, R.F., Li, M.C., Albishari, M., Zheng, F.C., Lan, Z.Z.: Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation. Appl. Math. Comput. 403, 126201 (2021)

    MathSciNet  MATH  Google Scholar 

  20. Zhang, R.F., Li, M.C., Fang, T., Zheng, F.C., Bilige, S.: Multiple exact solutions for the dimensionally reduced p-gBKP equation via bilinear neural network method. Mod. Phys. Lett. B 36, 2150590 (2022)

    MathSciNet  Google Scholar 

  21. Zhang, R.F., Li, M.C., Cherraf, A., et al.: The interference wave and the bright and dark soliton for two integro-differential equation by using BNNM. Nonlinear Dyn. (2023). https://doi.org/10.1007/s11071-023-08257-5

    Article  Google Scholar 

  22. Geng, K.L., Mou, D.S., Dai, C.Q.: Nondegenerate solitons of 2-coupled mixed derivative nonlinear Schrodinger equations. Nonlinear Dyn 111, 603–617 (2023)

    Google Scholar 

  23. Dai, C.Q., Zhang, J.F.: Exact spatial similaritons and rogons in 2D graded-index waveguides. Opt. Lett. 35, 2651–2653 (2010)

    Google Scholar 

  24. Akhmediev, N., Ankiewicz, A., Soto-Crespo, J.M.: Rogue waves and rational solutions of the nonlinear Schrodinger equation. Phys. Rev. E 80, 026601 (2009)

    Google Scholar 

  25. Draper, L.: Freak wave. Mar. Obs. 32, 193 (1965)

    Google Scholar 

  26. Dai, C.Q., Wang, Y.Y.: Controllable combined Peregrine soliton and Kuznetsov-Ma soliton in PT-symmetric nonlinear couplers with gain and loss. Nonlinear Dyn. 80, 715–721 (2015)

    MathSciNet  Google Scholar 

  27. Zhang, R.F., Li, M.C., Yin, H.M.: Rogue wave solutions and the bright and dark solitons of the (3+1)-dimensional Jimbo-Miwa equation. Nonlinear Dyn. 103, 1071–1079 (2021)

    Google Scholar 

  28. Zhang, R.F., Li, M.C., Al-Mosharea, E., Zheng, F.C., Bilige, S.: Rogue waves, classical lump solutions and generalized lump solutions for Sawada–Kotera-like equation. Int. J. Mod. Phys. B 36, 2250044 (2022)

    Google Scholar 

  29. Vinayagam, P.S., Radha, R., Porsezian, K.: Taming rogue waves in vector Bose–Einstein condensates. Phys. Rev. E 88, 042906 (2013)

    Google Scholar 

  30. Wang, Y.Y., Li, J.T., Dai, C.Q., Zhang, J.F.: Solitary waves and rogue waves in a plasma with nonthermal electrons featuring Tsallis distribution. Phys. Lett. A 377, 2097–2104 (2013)

    MathSciNet  MATH  Google Scholar 

  31. Akhmediev, N., Ankiewicz, A., Taki, M.: Waves that appear from nowhere and disappear without a trace. Phys. Lett. A 373, 675 (2009)

    MATH  Google Scholar 

  32. Ankiewicz, A., Sotocrespo, J.M., Akhmediev, N.: Rogue waves and rational solutions of the Hirota equation. Phys. Rev. E 81, 046602 (2010)

    MathSciNet  Google Scholar 

  33. Dai, C.Q., Zhou, G.Q., Zhang, J.F.: Controllable optical rogue waves in the femtosecond regime. Phys. Rev. E 85, 016603 (2012)

    Google Scholar 

  34. Chen, S.H., Mihalache, D.: Vector rogue waves in the Manakov system: diversity and compossibility. J. Phys. A Math. Theor. 48, 215202 (2015)

    MathSciNet  MATH  Google Scholar 

  35. Ankiewicz, A., Kedziora, D.J., Akhmediev, N.: Rogue wave triplets. Phys. Lett. A 375, 2782–2785 (2011)

    MATH  Google Scholar 

  36. Chabchoub, A., Hoffmann, N.P., Akhmediev, N.: Rogue wave observation in a water wave tank. Phys. Rev. Lett. 106, 204502 (2011)

    Google Scholar 

  37. Chabchoub, A., Hoffmann, N., Branger, H., Kharif, C., Akhmediev, N.: Experiments on wind-perturbed rogue wave hydrodynamics using the Peregrine breather model. Phys. Fluids 25, 101704 (2013)

    Google Scholar 

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

    Google Scholar 

  39. Lecaplain, C., Grelu, P., Soto-Crespo, J.M., Akhmediev, N.: Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser. Phys. Rev. Lett. 108, 233901 (2012)

    Google Scholar 

  40. Kumar, C.N., Gupta, R., Goyal, A., Loomba, S.: Controlled giant rogue waves in nonlinear fiber optics. Phys. Rev. A 86, 025802 (2012)

    Google Scholar 

  41. 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)

    Google Scholar 

  42. Xu, S.L., Belic, M.R.: Three-dimensional Hermite-Bessel solitons in strongly nonlocal media with variable potential coefficients. Opt. Commun. 313, 62–69 (2014)

    Google Scholar 

  43. 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)

    MathSciNet  MATH  Google Scholar 

  44. 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)

    Google Scholar 

  45. Chen, Y.X., Xiao, X.: Vector soliton pairs for a coupled nonautonomous NLS model with partially nonlocal coupled nonlinearities under the external potentials. Nonlinear Dyn. 109, 2003–2012 (2022)

    Google Scholar 

  46. Maruno, K., Ohta, Y.: Localized solitons of a (2 +1)-dimensional nonlocal nonlinear Schrödinger equation. Phys. Lett. A 372, 4446–4450 (2008)

    MATH  Google Scholar 

  47. 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)

    Google Scholar 

  48. Dai, C.Q., Wang, Y.Y., Zhang, J.F.: Managements of scalar and vector rogue waves in a partially nonlocal nonlinear medium with linear and harmonic potentials. Nonlinear Dyn. 102, 379–391 (2020)

    Google Scholar 

  49. Dai, C.Q., Zhang, J.F.: Controlling effect of vector and scalar crossed double-Ma breathers in a partially nonlocal nonlinear medium with a linear potential. Nonlinear Dyn. 100, 1621–1628 (2020)

    Google Scholar 

  50. Yang, J., Zhu, Y., Qin, W., Wang, S., Dai, C., Li, J.: Higher-dimensional soliton structures of a variable-coefficient Gross-Pitaevskii equation with the partially nonlocal nonlinearity under a harmonic potential. Nonlinear Dyn. 108, 2551–2562 (2022)

    Google Scholar 

  51. Zhu, H.P., Xu, Y.J.: High-dimensional vector solitons for a variable-coefficient partially nonlocal coupled GrossCPitaevskii equation in a harmonic potential. Appl. Math. Lett. 124, 107701 (2022)

    MATH  Google Scholar 

  52. Chen, S.H., Mihalache, D.: Vector rogue waves in the Manakov system: diversity and compossibility. J. Phys. A Math. Theor. 48, 215202 (2015)

    MathSciNet  MATH  Google Scholar 

  53. Yang, R.C., Hao, R.Y., Li, L., Shi, X.J., Li, Z.H., Zhou, G.S.: Exact gray multi-soliton solutions for nonlinear Schrodinger equation with variable coefficients. Opt. Commun. 253, 177–185 (2005)

    Google Scholar 

  54. 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)

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11975197).

Author information

Authors and Affiliations

  1. School of Electronics Information, Communication University of Zhejiang, Hangzhou, 310018, People’s Republic of China

    Yi-Xiang Chen

Authors
  1. Yi-Xiang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Yi-Xiang Chen: Writing- draft & review & editing, Investigation, Methodology.

Corresponding author

Correspondence to Yi-Xiang Chen.

Ethics declarations

Conflict of interest

The authors have declared that no conflict of interest exists.

Humans or animal rights

This article does not contain any studies with human or animal subjects.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, YX. Versatile excitations of 3D partially nonlocal bright–bright Peregrine-quartets in a nonautonomous vector nonlinear Schrödinger equation under a parabolic potential. Nonlinear Dyn 111, 11437–11446 (2023). https://doi.org/10.1007/s11071-023-08416-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-08416-8

Keywords

Search

Navigation