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The pair-transition-coupled nonlinear Schrödinger equation: The Riemann-Hilbert problem and N-soliton solutions

  • Xiu-Bin WangEmail author
  • Bo Han
Regular Article
  • 43 Downloads

Abstract.

In this work, the pair-transition-coupled nonlinear Schrödinger (pt-CNLS) equation, which can also be used to describe the propagation of orthogonally polarized optical waves in an isotropic medium, is under investigation. The spectral analysis with 4×4 Lax pairs is performed for the integrable pt-CNLS equations, from which a kind of Riemann-Hilbert problem is strictly formulated. Moreover, N-soliton solutions to the pt-CNLS equation are constructed by using a specific Riemann-Hilbert formulation.

References

  1. 1.
    G.P. Agrawal, Nonlinear Fiber Optics, 5th edition (Academic Press, New York, NY, 2012)Google Scholar
  2. 2.
    B.A. Alomed, D. Mihalache, F. Wise, L. Torner, J. Opt. B 7, R53 (2005)CrossRefGoogle Scholar
  3. 3.
    L. Pitaevskii, S. Stringari, Bose-Einstein Condensation and Superfluidity (Oxford University Press, Oxford, UK, 2016)Google Scholar
  4. 4.
    V.E. Zakharov, A.B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971)Google Scholar
  5. 5.
    H. Bailung, Y. Nakamura, J. Plasma Phys. 50, 231 (1993)ADSCrossRefGoogle Scholar
  6. 6.
    B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, J.M. Dudley, Sci. Rep. 2, 463 (2012)ADSCrossRefGoogle Scholar
  7. 7.
    Z. Yan, Commun. Theor. Phys. 54, 947 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    J. Soto-Crespo, N. Devine, N. Hoffmann, N. Akhmediev, Phys. Rev. E 90, 032902 (2014)ADSCrossRefGoogle Scholar
  9. 9.
    C. Lecaplain, P. Grelu, Phys. Rev. A 90, 013805 (2014)ADSCrossRefGoogle Scholar
  10. 10.
    B.A. Malomed, Phys. Rev. A 45, R8321 (1992)ADSCrossRefGoogle Scholar
  11. 11.
    Q.H. Park, H.J. Shin, Phys. Rev. E 59, 2373 (1999)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    L.C. Zhao, L. Ling, Z.Y. Yang, J. Liu, Commun. Nonlinear Sci. Numer. Simul. 23, 21 (2015)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    X. Lü, B. Tian, Phys. Rev. E 85, 026117 (2012)ADSCrossRefGoogle Scholar
  14. 14.
    L. Ling, L.C. Zhao, Phys. Rev. E 92, 022924 (2015)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    X.B. Wang, S.F. Tian, T.T. Zhang, Proc. Am. Math. Soc. 146, 3353 (2018)CrossRefGoogle Scholar
  16. 16.
    X.B. Wang, T.T. Zhang, M.J. Dong, Appl. Math. Lett. 86, 298 (2018)MathSciNetCrossRefGoogle Scholar
  17. 17.
    A.S. Fokas, A Unified Approach to Boundary Value Problems (SIAM, 2008)Google Scholar
  18. 18.
    W.X. Ma, J. Geom. Phys. 132, 45 (2018)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    X.B. Wang, B. Han, Z. Naturforsch. A 74, 139 (2018)ADSCrossRefGoogle Scholar
  20. 20.
    W.X. Ma, M. Chen, Appl. Math. Comput. 215, 2835 (2009)MathSciNetGoogle Scholar
  21. 21.
    W.X. Ma, J. Phys. Soc. Jpn. 72, 3017 (2003)ADSCrossRefGoogle Scholar
  22. 22.
    D.S. Wang, D.J. Zhang, J. Yang, J. Math. Phys. 51, 023510 (2010)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    D.S. Wang, S. Yin, Y. Tian, Y. Liu, Appl. Math. Comput. 229, 296 (2014)MathSciNetGoogle Scholar
  24. 24.
    D.S. Wang, X.L. Wang, Nonlinear Anal. Real World Appl. 41, 334 (2018)MathSciNetCrossRefGoogle Scholar
  25. 25.
    B.B. Hu, T.C. Xia, W.X. Ma, Appl. Math. Comput. 332, 148 (2018)MathSciNetGoogle Scholar
  26. 26.
    B.B. Hu, T.C. Xia, N. Zhang, J.B. Wang, Int. J. Nonlinear Sci. Numer. Simul. 19, 83 (2018)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Z.Z. Kang, T.C. Xia, X. Ma, Chin. Phys. Lett. 35, 070201 (2018)ADSCrossRefGoogle Scholar
  28. 28.
    X.B. Wang, S.F. Tian, L.L. Feng, T.T. Zhang, J. Math. Phys. 59, 073505 (2018)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    X. Geng, J. Wu, Wave Motion 60, 62 (2016)MathSciNetCrossRefGoogle Scholar
  30. 30.
    D. Kaup, J. Yang, Inverse Probl. 25, 105010 (2009)ADSCrossRefGoogle Scholar
  31. 31.
    J. Yang, Nonlinear Waves in Integrable and Non-integrable Systems (SIAM, 2010)Google Scholar
  32. 32.
    J. Yang, D. Kaup, J. Math. Phys. 50, 121 (2009)Google Scholar
  33. 33.
    Y.S. Zhang, Y. Cheng, J.S. He, J. Nonlinear Math. Phys. 24, 210 (2017)MathSciNetCrossRefGoogle Scholar
  34. 34.
    S.F. Tian, J. Differ. Equ. 262, 506 (2017)ADSCrossRefGoogle Scholar
  35. 35.
    S.F. Tian, J. Phys. A 50, 395204 (2017)MathSciNetCrossRefGoogle Scholar
  36. 36.
    S.F. Tian, Proc. R. Soc. London A 472, 20160588 (2016)ADSCrossRefGoogle Scholar
  37. 37.
    J. Williams, R. Walser, J. Cooper, E. Cornell, M. Holland, Phys. Rev. A 61, 033612 (2000)ADSCrossRefGoogle Scholar
  38. 38.
    G. Zhang, Z. Yan, X.Y. Wen, Proc. R. Soc. A 473, 20170243 (2017)ADSCrossRefGoogle Scholar
  39. 39.
    A.S. Fokas, J. Lenells, J. Phys. A 45, 195201 (2012)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    B. Bilman, L. Ling, P.D. Miller, arXiv:1806.00545 (2018)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of TechnologyHarbinChina

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