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

Abdullaev, A. S.

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

Keywords:

asymptotic behavior; decreasing self similar solutions; sine-Gordon equation

Citations:

Zbl 0554.34032