Its, A. R.; Petrov, V. E. “Isomonodromic” solutions of the sine-Gordon equation and the time asymptotics of its rapidly decreasing solutions. (English. Russian original) Zbl 0588.35076 Sov. Math., Dokl. 26, 244-247 (1982); translation from Dokl. Akad. Nauk SSSR 265, 1302-1306 (1982). From the authors’ Introduction: This note is a further development of the approach proposed by the first author in [Dokl. Akad. Nauk SSSR 261, 14- 18 (1981; Zbl 0534.35028)] for the calculation of the asymptotics of solutions of nonlinear equations integrable by the method of the inverse scattering problem. The basis for this approach is the concept of an ”isomonodromic solution” of the Zakharov-Shabat equation which arises naturally as a synthesis of the ideas of [I. M. Krichever, Funct. Anal. Appl. 14, 234-236 (1980; Zbl 0454.35078)] and [M. Jimbo, T. Miwa and K. Veno, Res. Inst. Math. Sci., Kyoto, preprint No.139 (1980)]. Reviewer: N.D.Kazarinoff Cited in 2 Documents MSC: 35Q99 Partial differential equations of mathematical physics and other areas of application 35P25 Scattering theory for PDEs 35J10 Schrödinger operator, Schrödinger equation 35L67 Shocks and singularities for hyperbolic equations Keywords:Korteweg de-Vries equation; sine-Gordon equation; asymptotics; nonlinear equations; inverse scattering; isomonodromic solution; Zakharov-Shabat Citations:Zbl 0534.35028; Zbl 0454.35078 PDFBibTeX XMLCite \textit{A. R. Its} and \textit{V. E. Petrov}, Sov. Math., Dokl. 26, 244--247 (1982; Zbl 0588.35076); translation from Dokl. Akad. Nauk SSSR 265, 1302--1306 (1982)