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

In: Lobachevsky Geometry and Modern Nonlinear Problems

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  • Andrey Popov

    (Lomonosov Moscow State University, Department of Mathematics)

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.

Suggested Citation

  • Andrey Popov, 2014. "The sine-Gordon equation: its geometry and applications of current interest," Springer Books, in: Lobachevsky Geometry and Modern Nonlinear Problems, edition 127, chapter 0, pages 127-223, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-05669-2_4
    DOI: 10.1007/978-3-319-05669-2_4
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