## Asymptotics of solutions of the generalized sine-Gordon equation, Painlevé’s third equation and d’Alembert’s equation.(English. Russian original)Zbl 0612.35115

Sov. Math., Dokl. 31, 45-47 (1985); translation from Dokl. Akad. Nauk SSSR 280, 265-268 (1985).
Using the technique of his paper [ibid. 28, 726-729 (1983); translation from Dokl. Akad. Nauk SSSR 273, 1033-1036 (1983; Zbl 0554.34032)] the author studies the asymptotic behavior as $$x\to \infty$$ of the decreasing self similar solutions of the generalized sine-Gordon equation $\partial^ 2u/\partial z\partial t=\nu \sin u+\mu zt \sin 2u\quad (x=zt).$
Reviewer: V.Vasil’ev

### MSC:

 35Q99 Partial differential equations of mathematical physics and other areas of application 35B40 Asymptotic behavior of solutions to PDEs 35C20 Asymptotic expansions of solutions to PDEs

Zbl 0554.34032