# zbMATH — the first resource for mathematics

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)
Full Text: