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Notes on periodic solitons
Author(s) -
Bakas I.,
Sourdis C.
Publication year - 2002
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/1521-3978(200209)50:8/9<815::aid-prop815>3.0.co;2-z
Subject(s) - simple (philosophy) , classical mechanics , rotation (mathematics) , sine , space (punctuation) , libration (molecule) , mathematical analysis , mathematics , physics , geometry , philosophy , linguistics , point (geometry) , epistemology
We consider static solutions of the sine‐Gordon theory defined on a cylinder, which can be either periodic or quasi‐periodic in space. They are described by the different modes of a simple pendulum moving in an inverted effective potential and correspond to its libration or rotation. We review the decomposition of the solutions into an oscillatory sum of alternating kinks and anti‐kinks or into a monotonic train of kinks, respectively, using properties of elliptic functions. The two sectors are naturally related to each other by a modular transformation, whereas the underlying spectral curve of the model can be used to express the energy of the static con.gurations in terms of contour integrals à la Seiberg‐Witten in either case. The stability properties are also examined by means of supersymmetric quantum mechanics, where we find that the unstable con.gurations are associated to singular superpotentials, thus allowing for negative modes in the spectrum of small fluctuations.