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Higher-dimensional vector two-component solitons of a nonautonomous partially nonlocal coupled NLS model in a linear and harmonic potential

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Abstract

A nonautonomous (\(3+1\))-dimensional partially nonlocal coupled NLS model in a linear and harmonic potential becomes the center of attention. Two kinds of reductions from this nonautonomous coupled equation into (\(1+1\))D and (\(2+1\))D constant-coefficient coupled ones are elucidated. Utilizing these solutions of constant-coefficient coupled equations via the Hirota’s bilinearization method, and by means of two kinds of reductions, two families of higher-dimensional vector two-component soliton solutions are deduced, including bright–dark vector two-component one-soliton solution and two-soliton solution, and vector two-component first-order localized soliton solution. Expansion and compression of these higher-dimensional vector two-component solitons are unfolded in the exponential diffraction system with the periodic modulation.

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Data availability statement: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Wazwaz, A.M.: A variety of multiple-soliton solutions for the integrable (4+1)-dimensional Fokas equation. W. Random and Complex Media 31, 46–56 (2021)

    Article  MathSciNet  Google Scholar 

  2. 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 Tech. 152, 108103 (2022)

    Article  Google Scholar 

  3. Dai, C.Q., Wang, Y.Y., Fan, Y., Zhang, J.F.: Interactions between exotic multi-valued solitons of the (2+1)-dimensional Korteweg-de Vries equation describing shallow water wave. Appl. Math. Model. 80, 506–515 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cao, Q.H., Dai, C.Q.: Symmetric and anti-symmetric solitons of the fractional second- and third-order nonlinear schrodinger equation. Chin. Phys. Lett. 38, 090501 (2021)

    Article  Google Scholar 

  5. Zhu, H.P., Chen, H.Y.: Parameter regulation for periodic wave pair and photovoltaic soliton pair excitations in the bias photovoltaic-photorefractive crystal. Results in Phys. 30, 104872 (2021)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  7. 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 Tech. 155, 108428 (2022)

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. 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)

    Article  MathSciNet  Google Scholar 

  10. 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)

    Article  MathSciNet  Google Scholar 

  11. Wen, X.K., Wu, G. Z., Liu, W., Dai, C.Q.: Dynamics of diverse data-driven solitons for the three-component coupled nonlinear Schrödinger model by the MPS-PINN method. Nonlinear Dyn. 109, 3041–3050 (2022)

  12. Chen, Y.X.: Combined optical soliton solutions of a (1+1)-dimensional time fractional resonant cubic-quintic nonlinear Schrödinger equation in weakly nonlocal nonlinear media. Optik 203, 163898 (2020)

    Article  Google Scholar 

  13. 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)

    Article  Google Scholar 

  14. 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)

    Article  MathSciNet  Google Scholar 

  15. 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)

    Article  MathSciNet  Google Scholar 

  16. Wen, L., Guo, H., Wang, Y.J., Hu, A.Y., Saito, H., Dai, C.Q., Zhang, X.F.: Effects of atom numbers on the miscibility-immiscibility transition of a binary Bose-Einstein condensate. Phys. Rev. A 101, 033610 (2020)

    Article  Google Scholar 

  17. Lu, P.H., Zhang, X.F., Dai, C.Q.: Dynamics and formation of vortices collapsed from ring dark solitons in a two-dimensional spin-orbit coupled Bose-Einstein condensate. Front. Phys. 17, 42501 (2022)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  19. Yan, Z.Y.: Rogon-like solutions excited in the two-dimensional nonlocal nonlinear Schrödinger equation. J. Math. Anal. Appl. 380, 689–696 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. 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)

    Article  MathSciNet  MATH  Google Scholar 

  21. 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)

    Article  Google Scholar 

  22. Chen, Y.X., Ou-Yang, F.Y.: Excitation management of crossed Akhmediev and Ma breather for a nonautonomous partially nonlocal Gross-Pitaevskii equation with an external potential. Nonlinear Dyn. 100, 1543–1550 (2020)

    Article  Google Scholar 

  23. 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)

    Article  Google Scholar 

  24. Wu, H.Y., Jiang, L.H.: Excitation management of (2+1)-dimensional breathers for a coupled partially nonlocal nonlinear Schrodinger equation with variable coefficients. Nonlinear Dyn. 95, 3401–3409 (2019)

    Article  MATH  Google Scholar 

  25. 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)

    Article  Google Scholar 

  26. Yang, J., Zhu, Y., Qin, W., Wang, S., Li, J.: Spatiotemporal vector vortex and diploe solitons of a nonautonomous partially nonlocal coupled Gross-Pitaevskii equation with a linear potential. Results in Phys. 30, 104860 (2021)

    Article  Google Scholar 

  27. Chen, Y.X., Xiao, X.: Vector brightCdark one-soliton and two-soliton of the coupled NLS model with the partially nonlocal nonlinearity in BEC. Optik 257, 168708 (2022)

    Article  Google Scholar 

  28. Vijayajayanthi, M., Kanna, T., Lakshmanan, M.: Bright-dark solitons and their collisions in mixed N-coupled nonlinear Schrodinger equations. Phys. Rev. A 77, 013820 (2008)

    Article  Google Scholar 

  29. Zhong, W.P., Belic, M., 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 

  30. 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)

    Article  Google Scholar 

  31. 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. Proc. of SPIE 4271, 292–302 (2001)

    Article  Google Scholar 

  32. Dai, C.Q., Wang, X.G., Zhou, G.Q.: Stable light-bullet solutions in the harmonic and parity-time-symmetric potentials. Phys. Rev. A 89, 013834 (2014)

    Article  Google Scholar 

  33. 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)

    Article  Google Scholar 

  34. Hao, R.Y., Li, L., Li, Z.H., Xue, W.R., Zhou, G.S.: A new approach to exact soliton solutions and soliton interaction for the nonlinear Schrodinger equation with variable coefficients. Opt. Commun. 236, 79–86 (2004)

    Article  Google Scholar 

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Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 11975008).

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Authors and Affiliations

  1. Vocational and Technical College, Lishui University, Lishui, 323000, Zhejiang, China

    Hai-Yan Chen

  2. College of Engineering, Lishui University, Lishui, 323000, Zhejiang, China

    Hai-Ping Zhu

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  1. Hai-Yan Chen
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Correspondence to Hai-Yan Chen.

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Chen, HY., Zhu, HP. Higher-dimensional vector two-component solitons of a nonautonomous partially nonlocal coupled NLS model in a linear and harmonic potential. Nonlinear Dyn 111, 581–590 (2023). https://doi.org/10.1007/s11071-022-07629-7

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  • DOI: https://doi.org/10.1007/s11071-022-07629-7

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