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Excitation management of crossed Akhmediev and Ma breather for a nonautonomous partially nonlocal Gross–Pitaevskii equation with an external potential

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Abstract

A nonautonomous Gross–Pitaevskii equation with a partially nonlocal nonlinearity and a linear and parabolic potential is discussed, and a projecting expression between nonautonomous and autonomous equations is found. Via the projecting expression and utilizing the Darboux transformation method, diversified exact solutions, especially including a crossed Akhmediev and Ma breather solution, are engendered. The parabolic and linear potentials influence the phase chirp and linear phase, respectively. By selecting values of diffraction, phase chirp and initial width parameters of wave to vary the maximum value of the accumulated time, the excitation management of the crossed Akhmediev and Ma breather, including the excitations of full shape, climax shape and early shape for different parts of the crossed Akhmediev and Ma breather, is achieved.

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References

  1. Chen, S.J., Yin, Y.H., Ma, W.X., Lv, X.: Abundant exact solutions and interaction phenomena of the (2 + 1)-dimensional YTSF equation. Anal. Math. Phys. 9, 2329–2344 (2019)

    Article  MathSciNet  Google Scholar 

  2. Dai, C.Q., Fan, Y., Zhang, N.: Re-observation on localized waves constructed by variable separation solutions of (1+1)-dimensional coupled integrable dispersionless equations via the projective Riccati equation method. Appl. Math. Lett. 96, 20–26 (2019)

    Article  MathSciNet  Google Scholar 

  3. Xu, H.N., Ruan, W.Y., Zhang, Y., Lv, X.: Multi-exponential wave solutions to two extended Jimbo–Miwa equations and the resonance behavior. Appl. Math. Lett. 99, 105976 (2020)

    Article  MathSciNet  Google Scholar 

  4. 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  Google Scholar 

  5. Chen, S.J., Ma, W.X., Lv, X.: Backlund transformation, exact solutions and interaction behaviour of the (3 + 1)-dimensional Hirota–Satsuma–Ito-like equation. Commun. Nonlinear Sci. Numer. Simul. 83, 105135 (2020)

    Article  MathSciNet  Google Scholar 

  6. Yin, Y.H., Ma, W.X., Guo, B.L., Lv, X., Liu, Wen-Xiu MaJian-Guo, Xing, L.: Diversity of exact solutions to a (3+1)-dimensional nonlinear evolution equation and its reduction. Comput. Math. Appl. 76, 1275–1283 (2018)

    Article  MathSciNet  Google Scholar 

  7. Anderson, M.H., Ensher, J.R., Matthews, M.R., Wieman, C.E., Cornell, E.A.: Observation of Bose–Einstein condensation in a dilute atomics vapor. Science 269, 198–201 (1995)

    Article  Google Scholar 

  8. Davis, K.B., Mewes, M.O., Andrews, M.R., Van Druten, N.J., Durfee, D.S., Kurn, D.M., Ketterle, W.: Bose–Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969 (1995)

    Article  Google Scholar 

  9. He, Z.M., Wen, L., Wang, Y.J., Chen, G.P., et al.: Dynamics and pattern formation of ring dark solitons in a two-dimensional binary Bose–Einstein condensate with tunable interactions. Phys. Rev. E 99, 062216 (2019)

    Article  Google Scholar 

  10. 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 

  11. 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 

  12. Wang, L.X., Dai, C.Q., Wen, L., Liu, T., et al.: Dynamics of vortices followed by the collapse of ring dark solitons in a two-component Bose–Einstein condensate. Phys. Rev. A 97, 063607 (2018)

    Article  Google Scholar 

  13. Chen, Y.X., Zheng, L.H., Xu, F.Q.: Spatiotemporal vector and scalar solitons of the coupled nonlinear Schrodinger equation with spatially modulated cubic-quintic-septimal nonlinearities. Nonlinear Dyn. 93, 2379–2388 (2018)

    Article  Google Scholar 

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

    Article  Google Scholar 

  15. 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 

  16. Wu, G.Z., Yu, L.J., Wang, Y.Y.: Fractional optical solitons of the space-time fractional nonlinear Schrödinger equation. Optik 207, 164405 (2020)

    Article  Google Scholar 

  17. Hua, Y.F., Guo, B.L., Ma, W.X., Lv, X.: Interaction behavior associated with a generalized (2 + 1)-dimensional Hirota bilinear equation for nonlinear waves. Appl. Math. Model. 74, 184–198 (2019)

    Article  MathSciNet  Google Scholar 

  18. 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)

    Article  MathSciNet  Google Scholar 

  19. 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 

  20. 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 

  21. Dai, C.Q., Wang, Y.Y., Fan, Y., Yu, D.G.: Reconstruction of stability for Gaussian spatial solitons in quintic-septimal nonlinear materials under PT-symmetric potentials. Nonlinear Dyn. 92, 1351–1358 (2018)

    Article  Google Scholar 

  22. Dai, C.Q., Fan, Y., Wang, Y.Y.: Three-dimensional optical solitons formed by the balance between different-order nonlinearities and high-order dispersion/diffraction in parity-time symmetric potentials. Nonlinear Dyn. 98, 489–499 (2019)

    Article  Google Scholar 

  23. Luo, Z., Li, Y., Pang, W., Liu, Y.: Dipolar matter-wave soliton in one-dimensional optical lattice with tunable local and nonlocal nonlinearities. J. Phys. Soc. Jpn. 82, 094401 (2013)

    Article  Google Scholar 

  24. Sarkar, S., Bhattacharyay, A.: Non-local interactions in a BEC: an analogue gravity perspective. J. Phys. A Math. Theor. 47, 092002 (2014)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  26. 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 

  27. Chen, Y.X., Xu, F.Q., Hu, Y.L.: Excitation control for three-dimensional Peregrine solution and combined breather of a partially nonlocal variable-coefficient nonlinear Schrödinger equation. Nonlinear Dyn. 95, 1957–1964 (2019)

    Article  Google Scholar 

  28. 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  Google Scholar 

  29. Chen, S.J., Lin, J.N., Wang, Y.Y.: Soliton solutions and their stabilities of three (2+1)-dimensional PT-symmetric nonlinear Schrodinger equations with higher-order diffraction and nonlinearities. Optik 194, 162753 (2019)

    Article  Google Scholar 

  30. Akhmediev, N., Korneev, V.I.: Modulation instability and periodic solutions of the nonlinear Schrodinger equation Theor. Math. Phys. 69, 1089–1093 (1986)

    MATH  Google Scholar 

  31. Ma, Y.C.: The perturbed plane-wave solution of the cubic Schrodinger equation. Stud. Appl. Math. 60, 43–58 (1979)

    Article  MathSciNet  Google Scholar 

  32. 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)

    Article  Google Scholar 

  33. Liu, Q.: Analytical matter wave solutions of a (2+1)-dimensional partially nonlocal distributed-coefficient Gross–Pitaevskii equation with a linear potential. Optik 200, 163434 (2020)

    Article  Google Scholar 

  34. Dai, C.Q., Tian, Q., Zhu, S.Q.: Controllable behaviours of rogue wave triplets in the nonautonomous nonlinear and dispersive system. J. Phys. B At. Mol. Opt. Phys. 45, 085401 (2012)

    Article  Google Scholar 

  35. 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 

  36. 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. SPIE 4271, 292–302 (2001)

    Article  Google Scholar 

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Acknowledgements

This work was supported by the NSFC (Grant Nos. 11975197 and 11775185).

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

    Yi-Xiang Chen & Fang-Yan Ou-Yang

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  1. Yi-Xiang Chen
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Correspondence to Yi-Xiang Chen.

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Chen, YX., Ou-Yang, FY. 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). https://doi.org/10.1007/s11071-020-05557-y

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