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Nonlinear partial difference equations. III: Discrete sine-Gordon equation. (English) Zbl 1334.39015
Summary: A nonlinear partial difference equation which reduces to the sine-Gordon equation in the continuum limit, is obtained and solved by the method of dependent variable transformation $$N$$-soliton solutions, the Bäcklund transformation and the inverse scattering form for this equation are presented.
For part II, cf. [ibid. 43, No. 6, 2074–2078 (1977; Zbl 1334.39014)].

##### MSC:
 39A12 Discrete version of topics in analysis 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 35Q53 KdV equations (Korteweg-de Vries equations)
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