Skip to main content
SpringerLink
Log in

Soliton surfaces

III. - Solvable nonlinearities with trivial geometry

  • Published:
Lettere al Nuovo Cimento (1971-1985)

Summary

It is shown that all soliton systems corresponding to the reductionr=−q of the ZS-AKNS spectral problem with an analytic at ϕ=0 dispersion relation express a trivial geometric fact: the Gaussian curvature of a plane is zero.

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

Footnotes

  1. G. L. Lamb: inBäcklund Transformations, edited byR. M. Miura (Springer, Berlin, Heidelberg, and New York, N. Y., 1976);I. N. Vekua:Principles of tensor analysis and theory of covariants (Moscow, 1978), in Russian;R. Sasaki:Phys. Lett. A,71, 390 (1979).

    Google Scholar 

  2. L. Dolan:Phys. Rev. D,15, 2337 (1977).

    Article  MathSciNet  ADS  Google Scholar 

  3. E. Witten:Phys. Lett.,38, 121 (1977).

    Article  Google Scholar 

  4. P. Forgacs, Z. Horväth andL. Palla:Ann. Phys. (N. Y.),136, 371 (1981).

    Article  ADS  Google Scholar 

  5. P. Forgacs, Z. Horväth andL. Palla:Phys. Rev. Lett.,45, 505 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  6. Ch. W. Misner:Phys. Rev. D,18, 4510 (1978).

    Article  MathSciNet  ADS  Google Scholar 

  7. A. Sym:Soliton theory is surface theory, preprint IFT-11-1981;A. Sym:Lett. Nuovo Cimento,33, 394 (1982) 1982).

  8. A. Sym:Lett. Nuovo Cimento,36, 307 (1983);D. Levi, A. Sym andS. Wojciechowski:Phys. Lett. A,94, 408 (1983).

    Article  MathSciNet  Google Scholar 

  9. M. J. Ablowitz et al.:Stud. Appl. Math.,53, 249 (1974);S. V. Manakov et al.:Theory of Solitons (Moscow, 1980), in Russian.

    MathSciNet  MATH  Google Scholar 

  10. H. Flaschka andA. C. Newell: inDynamical Systems, Theory and Applications, edited byJ. Moser (Springer, Berlin, 1975).

    Google Scholar 

  11. R. Gilmore:Lie Groups, Lie Algebras and Some of Their Applications (Wiley, New York, N. Y., 1974).

    MATH  Google Scholar 

  12. A. Sym:Soliton Surfaces IV. Topological Charge for nontopological solitions, preprint IFT-2-1984.

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics of Warsaw University, Hoza 69, 00-681, Warsaw, Poland

    A. Sym

Authors
  1. A. Sym
    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

Sym, A. Soliton surfaces. Lett. Nuovo Cimento 39, 193–196 (1984). https://doi.org/10.1007/BF02783669

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02783669

PACS. 02.20

PACS. 02.30

PACS. 02.40

Search

Navigation