Abstract
The boundary-value problem for a half plane for the elliptic sine-Gordon equation is solved using the inverse scattering method. The solution is applied to the theory of the stationary Josephson effect.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Barone and J. Paterno, The Josephson Effect. Physics and Application [Russian translation], Moscow (1984).
A. B. Borisov, G. G. Taluts, A. P. Tankeev, and G. V. Bezmaternykh, in: Current Problems in the Theory of Magnetism [in Russian], Kiev (1986), pp. 103–111.
J. M. Kosterlitz, J. Phys. C,7 1046 (1974).
O. Hudak, Phys. Lett. A,89 No. 5, 245–248 (1982).
A. Nakamura, J. Phys. Soc. Jpn.,52 No. 6, 1918–1920 (1983).
S. Takeno, Progr. Theor. Phys.,68 No. 3, 992–995 (1982).
D. Leibrandt, Phys. Rev. B,15 No. 7, 3353–3361 (1977).
V. D. Lipovskii and S. S. Nikulichev, Vestn. LGU Ser. Fiz. Khim., No. 4, 61–64 (1988).
L. A. Takhtadzhyan and L. D. Faddeev, Hamiltonian Approach in the Theory of Solitons [in Russian], Moscow (1986).
J. Ashkin and W. E. Lamb, Jr., Phys. Rev.64 159 (1943).
F. Dyson, E. Montrol, M. Kac, and M. Fisher, in: Stability and Phase Transitions [Russian translation], Moscow (1973), pp. 164–244.
R. K. Dodd, J. C. Eilbeck, J. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations, Academic Press, New York (1982).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akademii Nauk SSSR, Vol. 180, pp. 53–62, 1990.
Rights and permissions
About this article
Cite this article
Gutshabash, E.S., Lipovskii, V.D. Boundary-value problem for the two-dimensional elliptic sine-Gordon equation and its application to the theory of the stationary Josephson effect. J Math Sci 68, 197–201 (1994). https://doi.org/10.1007/BF01249332
Issue Date:
DOI: https://doi.org/10.1007/BF01249332