The sine-Gordon equation: its geometry and applications of current interest

Andrey Popov
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Andrey Popov: Lomonosov Moscow State University, Department of Mathematics

Chapter Chapter 3 in Lobachevsky Geometry and Modern Nonlinear Problems, 2014, pp 127-223 from Springer

Abstract: Abstract This chapter is devoted to geometrical aspects in the study of the sine-Gordon equation as a canonical (from the point of view of non-Euclidean hyperbolic geometry) nonlinear equation that has wide applications in contemporary mathematical physics. A far-reaching fact that enables the realization of diverse approaches to the investigation of problems connected with the sine-Gordon equation is the intimate association of this equation with surfaces of constant negative curvature, i.e., with pseudospherical surfaces.

Keywords: Cauchy Problem; Soliton Solution; Geodesic Curvature; Asymptotic Line; Irregular Singularity (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-05669-2_4

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DOI: 10.1007/978-3-319-05669-2_4

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