Poznyak, Eh. G.; Popov, A. G. Geometry of the sine-Gordon equation. (Russian) Zbl 0741.35072 Itogi Nauki Tekh., Ser. Probl. Geom. 23, 99-130 (1991). The first part of the paper contains an analysis of the integration methods of the sine-Gordon equation and geometrical interpretations of the solutions, the second part is devoted to studies of surfaces with constant negative curvature. The last part is concerned with the studies of surfaces with Gaussian curvature \(=-1\), leading to the general evolution principle for phenomena described by the sine-Gordon equation. Reviewer: A.Haimovici (Iaşi) Cited in 2 ReviewsCited in 8 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov) Keywords:integration methods; surfaces; curvature PDFBibTeX XMLCite \textit{Eh. G. Poznyak} and \textit{A. G. Popov}, Itogi Nauki Tekh., Ser. Probl. Geom. 23, 99--130 (1991; Zbl 0741.35072)