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Asymptotics of solutions of the generalized sine-Gordon equation, Painlevé’s third equation and d’Alembert’s equation. (English. Russian original) Zbl 0612.35115
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 $$ \partial\sp 2u/\partial z\partial t=\nu \sin u+\mu zt \sin 2u\quad (x=zt).$$
Reviewer: V.Vasil’ev
35Q99PDE of mathematical physics and other areas
35B40Asymptotic behavior of solutions of PDE
35C20Asymptotic expansions of solutions of PDE