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The sine-Gordon equation: geometry and physics. (Uravnenie sinus-Gordona: geometriya i fizika.) (Russian) Zbl 0790.53002

Novoe v Zhizni, Nauke, Tekhnike. Seriya Matematika, Kibernetika. 91-6. Moskva: Znanie. 45 p. (1991).
The paper consists of three sections (1. Basic notions of surface theory, 2. Pseudospherical surfaces vs sine-Gordon equation, 3. Applications) and a summary.

MSC:

53A05 Surfaces in Euclidean and related spaces
35L70 Second-order nonlinear hyperbolic equations
53-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry
35-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations
35Q53 KdV equations (Korteweg-de Vries equations)
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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