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)].
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) |
