Skip to main content
SpringerLink
Log in

A general method for the solution of nonlinear soliton and kink Schrödinger equations

  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

We present a method by which one-dimensional nonlinear soliton and kink Schrödinger equations can be solved in closed form. The hermitean nonlinear soliton operator may contain up to second derivatives of the wave function and the vanishing condition must hold. The method is applied to solve known nonlinear Schrödinger equations for one-soliton and one-kink solutions and, by inverting the procedure, to derive new operators with wave packet solutions of algebraic and arbitrary shapes. One of them is equivalent to the Derivative Nonlinear Schrödinger equation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Scott, A.C., Chu, F.Y.F., McLaughlin, D.W.: Proc. IEEE61, 1443 (1973)

    Google Scholar 

  2. Jackiw, R.: Rev. Mod. Phys.49, 681 (1977)

    Google Scholar 

  3. Benney, D.J., Newell, A.C.: J. Math. Phys.46, 133 (1967)

    Google Scholar 

  4. Nohl, C.R.: Ann. Phys. (NY)96, 234 (1976)

    Google Scholar 

  5. Rosen, G.: Phys. Rev.183, 1186 (1969)

    Google Scholar 

  6. Bialynicki-Birula, I., Mycielski, J.: Bull. Acad. Pol.23, 461 (1975)

    Google Scholar 

  7. Bialynicki-Birula, I., Mycielski, J.: Ann. Phys. (NY)100, 62 (1976)

    Google Scholar 

  8. Kawahara, T.: Kyoto Univ. preprint (1973), unpublished

  9. Mjolhus, E.: Plasma Phys.16, 321 (1976)

    Google Scholar 

  10. Mio, K., Ogino, T., Minami, K., Takeda, S.: J. Phys. Soc. Japan41, 265 (1976)

    Google Scholar 

  11. Kaup, D.J., Newell, A.C.: J. Math. Phys.19, 798 (1978)

    Google Scholar 

  12. Kawata, T., Kobayashi, N., Inoue, H.: J. Phys. Soc. Japan46, 1008 (1979)

    Google Scholar 

  13. Hirota, R.: J. Math. Phys.14, 805 (1973)

    Google Scholar 

  14. Fedyanin, V.K., Makhankov, V.G., Yakushevich, L.V.: Phys. Lett.61 A, 169 (1978)

    Google Scholar 

  15. Makhankov, V.G., Fedyanin, V.K.: Phys. Lett.68A, 169 (1978)

    Google Scholar 

  16. Vo Han Fuk, Chetverikov, V.M.: Teor. Mat. Fiz.36, 345 (1978); English transl. in Theor. Math. Phys.36, 779 (1979)

    Google Scholar 

  17. Pereira, N.R., Stenflo, L.: Phys. Fluids20, 1733 (1977)

    Google Scholar 

  18. Pereira, N.R.: Phys. Fluids20, 1735 (1977)

    Google Scholar 

  19. Gardner, C.S., Green, J.M., Kruskal, M.D., Miura, R.M.: Phys. Rev. Lett.19, 1095 (1967)

    Google Scholar 

  20. Watanabe, S., Miyakawa, M., Yajima, N.: J. Phys. Soc. Japan46, 1653 (1979)

    Google Scholar 

  21. Madelung, E.: Z. Physik40, 322 (1926)

    Google Scholar 

  22. Bohm, D.J.: Phys. Rev.85, 166 (1952)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sektion Physik, Universität München, Am Coulombwall 1, D-8046, Garching bei München, Germany

    Rainer W. Hasse

Authors
  1. Rainer W. Hasse
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hasse, R.W. A general method for the solution of nonlinear soliton and kink Schrödinger equations. Z Physik B 37, 83–87 (1980). https://doi.org/10.1007/BF01325508

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01325508

Keywords

Search

Navigation