Advertisement

Nonlinear Dynamics

, Volume 69, Issue 4, pp 1621–1630 | Cite as

Darboux transformation for an integrable generalization of the nonlinear Schrödinger equation

  • Xianguo Geng
  • Yanyan Lv
Original Paper

Abstract

A Darboux transformation for an integrable generalization of the coupled nonlinear Schrödinger equation is derived with the help of the gauge transformation between the Lax pair. As a reduction, a Darboux transformation for an integrable generalization of the nonlinear Schrödinger equation is obtained, from which some new solutions for the integrable generalization of the nonlinear Schrödinger equation are given.

Keywords

An integrable generalization of the nonlinear Schrodinger equation Darboux transformation Exact solutions 

Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Project no. 11171312).

References

  1. 1.
    Fokas, A.S.: On a class of physically important integrable equations. Physica D 87, 145–150 (1995) MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Lenells, L.: Exactly solvable model for nonlinear pulse propagation in optical fibers. Stud. Appl. Math. 123, 215–232 (2009) MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Lenells, L., Fokas, A.S.: On a novel integrable generalization of the nonlinear Schrödinger equation. Nonlinearity 22, 11–27 (2009) MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Lenells, L., Fokas, A.S.: An integrable generalization of the nonlinear Schrödinger equation on the half-line and solitons. Inverse Probl. 25, 115006 (2009) MathSciNetCrossRefGoogle Scholar
  5. 5.
    Lenells, L.: Dressing for a novel integrable generalization of the nonlinear Schrödinger equation. J. Nonlinear Sci. 20, 709–722 (2010) MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Matveev, V.B., Salle, M.A.: Darboux Transformations and Solitons. Springer, Berlin (1991) MATHGoogle Scholar
  7. 7.
    Levi, D.: On a new Darboux transformation for the construction of exact solutions of the Schrödinger equation. Inverse Probl. 4, 165–172 (1988) MATHCrossRefGoogle Scholar
  8. 8.
    Gu, C.H., Zhou, Z.X.: On Darboux transformations for soliton equations in high-dimensional spacetime. Lett. Math. Phys. 32, 1–10 (1994) MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Li, Y.S.: The reductions of the Darboux transformation and some solutions of the soliton equations. J. Phys. A 29, 4187–4195 (1996) MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Geng, X.G., Ham, H.W.: Darboux transformation and soliton solutions for generalized nonlinear Schrödinger equations. J. Phys. Soc. Jpn. 68, 1508–1542 (1999) MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of MathematicsZhengzhou UniversityZhengzhouPeople’s Republic of China

Personalised recommendations