This article is cited in 1 paper

Construction of exact solution to sine-Gordon equation on the base of its characteristic Lie ring

A. V. Zhiber^a, S. N. Kamaeva<sup>b

a</sup> Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
^b Ufa State Aviation Technical University

Abstract: In the work we consider the scheme of constructing exact solutions to the Sine-Gordon equation based on a restricting the characteristic Lie ring. We study in details the case when the dimension of the space formed by commutators of length $6$ is equal to $1$.

Keywords: solitons, vector fields, Lie ring.

UDC: 517.9

MSC: 34A05, 35B06

Received: 06.07.2016

 English version: Ufa Mathematical Journal, 2016, 8:3, 49–57

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