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Exact solution of the \(n\)-dimensional sine-Gordon equation. (English) Zbl 1334.35284
Summary: Exact solutions of the \(n\)-dimensional sine-Gordon equation are obtained and a mathematical meaning of R. Hirota’s condition [ibid. 33, 1459–1463 (1972); ibid. 35, 1566 (1973)] is explained. It is shown that an \(N\)-kink solution can also exist in this case.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
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