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Dynamical behaviour of solitons in a š¯’«š¯’Æ-invariant nonlocal nonlinear Schrƶdinger equation with distributed coefficients

  • KannanĀ Manikandan
  • SeenimuthuĀ Stalin
  • MurugaianĀ SenthilvelanEmail author
Regular Article
  • 48 Downloads

Abstract

We present one-, two- and three-soliton solutions of a parity-time (š¯’«š¯’Æ)-invariant nonlocal nonlinear Schrƶdinger (NNLS) equation with distributed coefficients, namely dispersion, nonlinearity and loss/gain parameters. We map the considered equation into constant coefficient š¯’«š¯’Æ-invariant NNLS equation with a constraint. We prove that the considered system is š¯’«š¯’Æ-invariant only when the distributed coefficients are even functions. To investigate the dynamical behaviour of the constructed one- and two-soliton solutions, we consider three different forms of dispersion parameters, namely (i) constant, (ii) periodically distributed, and (iii) exponentially distributed one. We report how the intensity profiles of solitons get modified in the background by considering the aforementioned dispersion parameters. By performing asymptotic analysis, we also explain how the dispersion parameters influence the interactions of nonlocal solitons.

Keywords

Statistical and Nonlinear PhysicsĀ 

References

  1. 1.
    M.J. Ablowitz, Z.H. Musslimani, Phys. Rev. Lett. 110, 064105 (2013) CrossRefGoogle Scholar
  2. 2.
    M.J. Ablowitz, Z.H. Musslimani, Nonlinearity 29, 915 (2016) MathSciNetCrossRefGoogle Scholar
  3. 3.
    M. Lin, T. Xu, Phys. Rev. E 91, 033202 (2015) MathSciNetCrossRefGoogle Scholar
  4. 4.
    X.Z. Xu, K.W. Chow, Appl. Math. Lett. 56, 72 (2016) MathSciNetCrossRefGoogle Scholar
  5. 5.
    X. Huang, L.M. Ling, Eur. Phys. J. Plus 131, 148 (2016) CrossRefGoogle Scholar
  6. 6.
    X.Y. Wen, Z.Y. Yan, Y.Q. Yang, Chaos 26, 063123 (2016) MathSciNetCrossRefGoogle Scholar
  7. 7.
    Z.Y. Yan, Appl. Math. Lett. 62, 101 (2016) MathSciNetCrossRefGoogle Scholar
  8. 8.
    Z.W. Wu, J.S. He, Rom. Rep. Phys. 68, 79 (2016) Google Scholar
  9. 9.
    W. Liu, D.Q. Qiu, Z.W. Wu, J.S. He, Commun. Theor. Phys. 65, 671 (2016) CrossRefGoogle Scholar
  10. 10.
    L.Y. Ma, Z.N. Zhu, J. Math. Phys. 57, 083507 (2016) MathSciNetCrossRefGoogle Scholar
  11. 11.
    M. Li, T. Xu, D.X. Meng, J. Phys. Soc. Jpn. 85, 124001 (2016) CrossRefGoogle Scholar
  12. 12.
    Y.X. Zhang, D.Q. Qiu, Y. Cheng, J.S. He, Rom. J. Phys. 62, 108 (2017) Google Scholar
  13. 13.
    A.K. Sarma, M.A. Miri, Z.H. Musslimani, D.N. Christodoulides, Phys. Rev. E 89, 052918 (2014) CrossRefGoogle Scholar
  14. 14.
    V.S. Gerdjikov, A. Saxena, J. Math. Phys. 58, 013502 (2017) MathSciNetCrossRefGoogle Scholar
  15. 15.
    B.F. Feng, X.D. Luo, M.J. Ablowitz, Z.H. Musslimani, https://doi.org/arXiv:1712.09172 (2017)
  16. 16.
    T.A. Gadzhimuradov, A.M. Agalarov, Phys. Rev. A 93, 062124 (2016) CrossRefGoogle Scholar
  17. 17.
    A.S. Fokas, Nonlinearity 29, 319 (2016) MathSciNetCrossRefGoogle Scholar
  18. 18.
    Z. Yan, Appl. Math. Lett. 47, 61 (2015) MathSciNetCrossRefGoogle Scholar
  19. 19.
    S.K. Gupta, A.K. Sarma, Commun. Nonlin. Sci. Numer. Simula. 36, 141 (2016) CrossRefGoogle Scholar
  20. 20.
    L.-Y. Ma, Z.-N. Zhu, Appl. Math. Lett. 59, 115 (2016) MathSciNetCrossRefGoogle Scholar
  21. 21.
    J.L. Ji, Z.N. Zhu, Commun. Nonlin. Sci. Numer. Simul. 42, 699 (2017) CrossRefGoogle Scholar
  22. 22.
    Z. Wen, Z. Yan, Chaos 27, 053105 (2017) MathSciNetCrossRefGoogle Scholar
  23. 23.
    F. Yu, Chaos 27, 023108 (2017) MathSciNetCrossRefGoogle Scholar
  24. 24.
    G. Zhang, Z. Yan, Euro. Phys. Lett. 118, 6000 (2017) Google Scholar
  25. 25.
    G. Zhang, Z. Yan, Y. Chen, Appl. Math. Lett. 69, 113 (2017) MathSciNetCrossRefGoogle Scholar
  26. 26.
    Y. Chen, Appl. Math. Lett. 79, 123 (2018) MathSciNetCrossRefGoogle Scholar
  27. 27.
    K. Chen, D.-j. Zhang, Appl. Math. Lett. 75, 82 (2018) MathSciNetCrossRefGoogle Scholar
  28. 28.
    W. Liu, Z. Qin, https://doi.org/arXiv:1711.06059 (2017)
  29. 29.
    J. Cen, F. Correa, A. Fring, https://doi.org/arXiv:1710.11560 (2017)
  30. 30.
    J. Rao, K. Porsezian, J.S. He, Stud. Appl. Math. 139, 568 (2017) MathSciNetCrossRefGoogle Scholar
  31. 31.
    J. Rao, Y. Cheng, J.S. He, Stud. Appl. Math. 139, 568 (2017) MathSciNetCrossRefGoogle Scholar
  32. 32.
    Y. Liu, D. Mihalache, J.S. He, Nonlinear Dyn. 90, 2445 (2017) CrossRefGoogle Scholar
  33. 33.
    X. Deng,S. Lou, D.-J. Zhang, https://doi.org/arXiv:1707.07253 (2017)
  34. 34.
    C. Song, D. Xiao, Z. N. Zhu, J. Phys. Soc. Jpn. 86, 054001 (2017) CrossRefGoogle Scholar
  35. 35.
    B. Yang,J. Yang, https://doi.org/arXiv:1705.00332 (2017)
  36. 36.
    T. Xu, H. Li, H. Zhang, M. Li, S. Lan, Appl. Math. Lett. 63, 88 (2017) MathSciNetCrossRefGoogle Scholar
  37. 37.
    H. Zhang, M. Zhang, R. Hu, Appl. Math. Lett. 76, 170 (2018) MathSciNetCrossRefGoogle Scholar
  38. 38.
    M. GĆ¼rses, Phys. Lett. A 381, 1791 (2017) MathSciNetCrossRefGoogle Scholar
  39. 39.
    V.S. Gerdjikov, D.G. Grahovski, R.I. Ivanov, Theor. Math. Phys. 188, 1305 (2016) CrossRefGoogle Scholar
  40. 40.
    M. GĆ¼rses, A. Pekcan, J. Math. Phys. 59, 051501 (2018) MathSciNetCrossRefGoogle Scholar
  41. 41.
    S. Stalin, M. Senthilvelan, M. Lakshmanan, https://doi.org/arXiv:1806.06729 (2018)
  42. 42.
    S. Stalin, M. Senthilvelan, M. Lakshmanan, https://doi.org/arXiv:1806.06735 (2018)
  43. 43.
    A.W. Snyder, D.J. Mitchell, Science 276, 1538 (1997) CrossRefGoogle Scholar
  44. 44.
    C. Conti, M. Peccianti, G. Assanto, Phys. Rev. Lett. 92, 113902 (2004) CrossRefGoogle Scholar
  45. 45.
    C.M. Bender, S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998) MathSciNetCrossRefGoogle Scholar
  46. 46.
    C.M. Bender, Rep. Prog. Phys. 70, 947 (2007) CrossRefGoogle Scholar
  47. 47.
    M. Mitchell, M. Segev, T.H. Coskun, D.N. Christodoulides, Phys. Rev. Lett. 79, 4990 (1997) CrossRefGoogle Scholar
  48. 48.
    A. Hasegawa, Y. Kodama, Solitons in optical communications (Clarendon, Oxford, 1995) Google Scholar
  49. 49.
    S. Stalin, M. Senthilvelan, M. Lakshmanan, Phys. Lett. A 381, 2380 (2017) MathSciNetCrossRefGoogle Scholar
  50. 50.
    S. Stalin, M. Senthilvelan, M. Lakshmanan, https://doi.org/arXiv:1709.00733 (2017)
  51. 51.
    K. Manikandan, N. Vishnu Priya, M. Senthilvelan, R. Sankaranarayanan, Chaos 28, 083103 (2018) MathSciNetCrossRefGoogle Scholar
  52. 52.
    V.N. Serkin, A. Hasegawa, T.L. Belyaeva, Phys. Rev. Lett. 98, 074102 (2007) CrossRefGoogle Scholar
  53. 53.
    V.N. Serkin, A. Hasegawa, T.L. Belyaeva, J. Mod. Opt. 57, 1456 (2012) CrossRefGoogle Scholar
  54. 54.
    Z. Yan, Phys. Lett. A 374, 672 (2010) CrossRefGoogle Scholar
  55. 55.
    C.Q. Dai, Y.Y. Wang, C.J. Yan, Opt. Commun. 283, 1489 (2010) CrossRefGoogle Scholar
  56. 56.
    C.N. Kumar, R. Gupta, A. Goyal, S. Loomba, Phys. Rev. A 86, 025802 (2012) CrossRefGoogle Scholar
  57. 57.
    K. Manikandan, P. Muruganandam, M. Senthilvelan, M. Lakshmanan, Phys. Rev. E 90, 062905 (2014) CrossRefGoogle Scholar
  58. 58.
    K. Manikandan, P. Muruganandam, M. Senthilvelan, M. Lakshmanan, Phys. Rev. E 93, 032212 (2016) MathSciNetCrossRefGoogle Scholar
  59. 59.
    S. Loomba, H. Kaur, R. Gupta, C.N. Kumar, T.S. Raju, Phys. Rev. E 89, 052915 (2014) CrossRefGoogle Scholar
  60. 60.
    K. Manikandan, M. Senthilvelan, R.A. Kraenkel, Euro. Phys. J. B 89, 30 (2016) CrossRefGoogle Scholar
  61. 61.
    K. Manikandan, M. Senthilvelan, R.A. Kraenkel, Euro. Phys. J. B 89, 218 (2016) CrossRefGoogle Scholar
  62. 62.
    K. Manikandan, M. Senthilvelan, Chaos 26, 073116 (2016) MathSciNetCrossRefGoogle Scholar
  63. 63.
    D. Sinha, P.K. Ghosh, Phys. Rev. E 91, 042908 (2015) MathSciNetCrossRefGoogle Scholar

Copyright information

Ā©Ā EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer NatureĀ 2018

Authors and Affiliations

  • KannanĀ Manikandan
    • 1
  • SeenimuthuĀ Stalin
    • 2
  • MurugaianĀ Senthilvelan
    • 2
    Email author
  1. 1.Department of PhysicsNational Institute of TechnologyTiruchirappalliIndia
  2. 2.Centre for Nonlinear Dynamics, School of Physics, Bharathidasan UniversityTiruchirappalliIndia

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