On some single-hump solutions of the short-pulse equation and their periodic generalizations

In the present work, we consider both localized (e.g. peakon and breather) and extended waveforms (peakon-lattice and breather-lattice, as well as some periodic ones) that arise in the context of the short-pulse equation, as emanating from their sine-Gordon equation analogs. Through direct numerical...

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Published inPhysics letters. A Vol. 374; no. 29; pp. 2964 - 2967
Main Authors Shen, Y., Williams, F., Whitaker, N., Kevrekidis, P.G., Saxena, A., Frantzeskakis, D.J.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 28.06.2010
Subjects
Direct numerical simulation
Emission
Instability
Mathematical analysis
Mathematical models
Solid state physics
Stability
Waveforms
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Summary:In the present work, we consider both localized (e.g. peakon and breather) and extended waveforms (peakon-lattice and breather-lattice, as well as some periodic ones) that arise in the context of the short-pulse equation, as emanating from their sine-Gordon equation analogs. Through direct numerical simulations, we find that the most robust solution is the breather, although some of the single-hump variants of the periodic solutions may be preserved upon the time dynamics as well. Multi-peakon, as well as multi-breather and multi-hump profiles more generally are found to be subject to symmetry-breaking instabilities and are, thus, less robust.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2010.05.014