Boundary-value problem for the two-dimensional elliptic sine-Gordon equation and its application to the theory of the stationary Josephson effect

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.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akademii Nauk SSSR, Vol. 180, pp. 53–62, 1990.