Skip to main content

On the multiply connectedness of level lines of n-soliton solutions of the sine-Gordon equation

Abstract

The behavior of level lines z = of multi-soliton solutions of the sine-Gordon equation is considered.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    P. L. Chebyshev, “Über den Schnitt von Bekleidungen,” Usp. Mat. Nauk, 1, No. 2, pp. 38–42 (1946).

    Google Scholar 

  2. 2.

    D. Hilbert, Foundations of Geometry [Russian translation], Moscow-Leningrad (1948).

  3. 3.

    E. N. Pelinovsky, “Some methods in the theory of nonlinear waves,” Radiophysics, 5, 883–901 (1976).

    Google Scholar 

  4. 4.

    E. G. Poznyak, “Geometric interpretation of regular solutions of the equation z xy = sin z,” Differ. Uravn., 15, No. 7, 1332–1336 (1979).

    MathSciNet  Google Scholar 

  5. 5.

    E. G. Poznyak and A. G. Popov, “Geometry of the sine-Gordon equation,” Probl. Geom., 23, 99–130 (1991).

    MathSciNet  Google Scholar 

Download references

Author information

Affiliations

Authors

Additional information

__________

Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry, 2005.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Viktorova, O.D. On the multiply connectedness of level lines of n-soliton solutions of the sine-Gordon equation. J Math Sci 141, 1081–1086 (2007). https://doi.org/10.1007/s10958-007-0036-2

Download citation

Keywords

  • Regular Solution
  • Soliton Solution
  • Level Line
  • Isometric Immersion
  • Constant Negative Curvature