UNSPECIFIED (1997) The disappearing soliton component of a perturbed sine-Gordon breather. PHYSICA D, 101 (1-2). pp. 95-115. ISSN 0167-2789

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Abstract

In this paper we study a particular solution to a perturbed sine-Gordon equation, possessing a coherence that suggests the presence of a breather in the scattering data. Our perturbation consists of a delta function, that pins a periodic oscillation at the origin. For small energies of oscillation, the oscillation is an excitation of the discrete state in the spectrum of the vacuum u = 0, with an inverse scattering transform consisting purely of continuum modes; the radiation spectrum has a coherence in the absence of any solitons, that reproduces the localised oscillation. As the energy of oscillation is increased, solitons are created. At higher energies, the solitons dominate, and the oscillation is well approximated by a breather. The perturbation allows an exact calculation of the inverse scattering transform; therefore the varying composition of the scattering data as a function of the energy of oscillation can be studied. We also examine two approximation methods, the perturbed inverse scattering method and a variational method, and compare their reproduction of the exact result.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	PHYSICA D
Publisher:	ELSEVIER SCIENCE BV
ISSN:	0167-2789
Date:	15 February 1997
Volume:	101
Number:	1-2
Number of Pages:	21
Page Range:	pp. 95-115
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/18017

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