Finite-gap solutions of the Sine-Gordon equation

2014/01/17 by Kotlarov, V. P.
#35Q53 #37K10 #Exactly Solvable and Integrable Systems (nlin.SI) #F.2.2 #FOS: Physical sciences #I.2.7

paper · doi:10.48550/arxiv.1401.4410

Abstract

This paper contains first results on the finite-gap integration of the Sine-Gordon equation. They were published on Russian in 1976. The papers \citeKoz, \citeKK, \citeKK02 have been rewritten in the English language with small modifications for a convenience. Such a translation was made due to requests of some interested readers. In those papers, the method of constructing of the finite-gap solutions of the equation u_tt-u_xx+sin u=0 was proposed. The explicit formulae were obtained for these solutions. The formulae are constructed in terms of θ-functions and they are analogous to the formulae obtained by A.R.Its and V.B.Matveev \citeIM, B.A.Dubrovin and S.P.Novikov \citeDN for periodic and almost periodic solutions to the Korteweg de Vries equation.

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