Kodai Mathematical Journal

A new interpretation of the Bäcklund transformation of the sine-Gordon equation

Ze-Jun Hu and Zhen-Zu Sun

Full-text: Open access

Article information

Source
Kodai Math. J., Volume 23, Number 1 (2000), 100-104.

Dates
First available in Project Euclid: 23 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1138044158

Digital Object Identifier
doi:10.2996/kmj/1138044158

Mathematical Reviews number (MathSciNet)
MR1749387

Zentralblatt MATH identifier
0955.35066

Subjects
Primary: 37K35: Lie-Bäcklund and other transformations
Secondary: 37K25: Relations with differential geometry 53A05: Surfaces in Euclidean space

Citation

Hu, Ze-Jun; Sun, Zhen-Zu. A new interpretation of the Bäcklund transformation of the sine-Gordon equation. Kodai Math. J. 23 (2000), no. 1, 100--104. doi:10.2996/kmj/1138044158. https://projecteuclid.org/euclid.kmj/1138044158


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References

  • [1] A. V BACKLUND, Concerning surfaces with constant negative curvature, Translated by E. M. Coddington, New Era Pnting Co., Lancaster, Pa., 1905.
  • [2] M. do CARMO, Differential Geometry of Curves and Surfaces, Prentice-Hall Inc., 1976
  • [3] S. S. CHERN, Geometrical interpretation of the sinh-Gordon equation, Ann. Polon. Math., 3 (1981), 63-69.
  • [4] S. S. CHERN AND C. L. TERNG, An analogue of Backlund's theorem in affine geometry, Rocky Mountain J. Math., 10 (1980), 105-124
  • [5] H. S. Hu, The construction of hyperbolic surfaces m 3-dimensional Minkowski space and sinh Laplace equation, Acta Math. Simca, 1 (1985), 79-86.
  • [6] W. KLINGENBERG, A Course in Differential Geometry, Grad. Texts in Math., 51, Spnger Verlag, 1978.
  • [7] K. TENENBLAT AND C. L. TERNG, Backlund theorem for ^-dimensional submanifolds of R2n~, Ann. of Math., 112 (1980), 477-490
  • [8] C. L. TERNG, A higher dimension generalization of the sine-Gordon equation and its solito theory, Ann. of Math., 112 (1980), 491-510.