Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus

12 Issues per year

IMPACT FACTOR 2016: 1.432

CiteScore 2017: 1.30

SCImago Journal Rank (SJR) 2017: 0.403
Source Normalized Impact per Paper (SNIP) 2017: 0.632

See all formats and pricing
More options …
Volume 72, Issue 1


Darboux Transformation for Coupled Non-Linear Schrödinger Equation and Its Breather Solutions

Lili Feng
  • School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, China
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Fajun Yu
  • Corresponding author
  • School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, China
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Li Li
  • School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang 110034, China
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-12-21 | DOI: https://doi.org/10.1515/zna-2016-0342


Starting from a 3×3 spectral problem, a Darboux transformation (DT) method for coupled Schrödinger (CNLS) equation is constructed, which is more complex than 2×2 spectral problems. A scheme of soliton solutions of an integrable CNLS system is realised by using DT. Then, we obtain the breather solutions for the integrable CNLS system. The method is also appropriate for more non-linear soliton equations in physics and mathematics.

Keywords: Coupled Schrödinger System; Darboux Transformation; Exact Solutions

PACS: 05.45.Yv; 42.65.Tk; 42.50.Gy


  • [1]

    M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, New York 1991.Google Scholar

  • [2]

    B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, et al., Nat. Phys. 6, 790 (2010).Google Scholar

  • [3]

    M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, et al. Phys. Rev. Lett. 107, 253901 (2011).Google Scholar

  • [4]

    G. P. Agrawal, Applications of Nonlinear Fiber, Academic, San Diego 2001.Google Scholar

  • [5]

    S. K. Adhikari, Phys. Rev. A. 63, 043611 (2001).Google Scholar

  • [6]

    A. Uthayakumar, Y. G. Han, and S. B. Lee, Chaos Solitons Fract. 29, 916 (2006).Google Scholar

  • [7]

    A. Hasegawa and Y. Kodama, Solitons in Optical Communications, Clarendon, Oxford 1995.Google Scholar

  • [8]

    G. J. Roskes, Stud. Appl. Math. 55, 231 (1976).Google Scholar

  • [9]

    F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999).Google Scholar

  • [10]

    D. S. Wang, D. J. Zhang, and J. K. Yang, J. Math. Phys. 51, 023510 (2010).Google Scholar

  • [11]

    N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams, Chapman and Hall, London 1997.Google Scholar

  • [12]

    Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals, Academic Press, New York 2003.Google Scholar

  • [13]

    M. P. Barnett, J. F. Capitani, J. Von Zur Gathen, and J. Gerhard, Int. J. Quantum Chem. 100, 80 (2004).Google Scholar

  • [14]

    V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons, Springer-Verlag, Berlin 1991.Google Scholar

  • [15]

    M. Wadati, J. Phys. Soc. Jpn. 38, 673 (1975).Google Scholar

  • [16]

    Y. T. Gao and B. Tian, Phys. Lett. A. 361, 523 (2007).Google Scholar

  • [17]

    J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 24, 522 (1983).Google Scholar

  • [18]

    R. Hirota, The Direct Method in Soliton Theory, Cambridge Univ. Press, Cambridge 2004.Google Scholar

  • [19]

    P. Deift and E. Trubowitz, Comm. Pure Appl. Math. 32, 121 (1979).Google Scholar

  • [20]

    C. H. Gu, H. S. Hu, and Z. Zhou, Darboux Transformations in Integrable Systems: Theory and Their Applications to Geometry, Springer, Berlin 2006.Google Scholar

  • [21]

    C. L. Terng and K. Uhlenbeck, Comm. Pure Appl. Math. 53, 1 (2000).Google Scholar

  • [22]

    S. P. Novikov, S. V. Manakov, V. E. Zakharov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Scattering Method, Springer, Berlin 1984.Google Scholar

  • [23]

    C. H. Gu, H. S. Hu, and Z. X. Zhou, Darboux Transform in Soliton Theory and Its Geometric Applications. Shanghai Scientific Technical Publishers, Shanghai 1999.Google Scholar

  • [24]

    H. Y. Ding, X. X. Xu, and X. D. Zhao, Chin. Phys. 13, 125 (2004).Google Scholar

  • [25]

    Y. T. Wu and X. G. Geng, J. Phys. A Math. Gen. 31, L677 (1998).Google Scholar

  • [26]

    X. X. Xu, H. X. Yang, and Y. P. Sun, Mod. Phys. Lett. B. 20, 641 (2006).Google Scholar

  • [27]

    X. X. Xu, Commun. Nonlinear. Sci. 23, 192 (2015).Google Scholar

  • [28]

    L. Wang, J. H. Zhang, C. Liu, M. Li, and F. H. Qi, Phys. Rev. E. 93, 062217 (2016).Google Scholar

  • [29]

    L. Wang, J. H. Zhang, Z. Q. Wang, C. Liu, M. Li, et al., Phys. Rev. E. 93, 012214 (2016).Google Scholar

  • [30]

    L. Wang, Y. J. Zhu, F. H. Qi, M. Li, and R. Guo, Chaos 25, 063111 (2015).Google Scholar

  • [31]

    L. Wang, X. Li, F. H. Qi, and L. L. Zhang, Ann. Phys. 359, 97 (2015).Google Scholar

  • [32]

    F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, Phys. Rev. Lett. 109, 044102 (2012).Google Scholar

  • [33]

    B. L. Guo and L. M. Ling, Chin. Phys. Lett. 28, 110202 (2011).Google Scholar

  • [34]

    S. V. Manakov. Sov. Phys. JETP 38, 248 (1974).Google Scholar

  • [35]

    P. K. A. Wai, C. R. Menyuk, and H. H. Chen, Opt. Lett. 16, 1231 (1991).Google Scholar

About the article

Received: 2016-09-06

Accepted: 2016-11-10

Published Online: 2016-12-21

Published in Print: 2017-01-01

Citation Information: Zeitschrift für Naturforschung A, Volume 72, Issue 1, Pages 9–15, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2016-0342.

Export Citation

©2017 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Comments (0)

Please log in or register to comment.
Log in