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On some single-hump solutions of the short-pulse equation and their periodic generalizations
Physics Letters A (2010)
  • Y Shen
  • F Williams
  • N Whitaker
  • PG Kevrekidis, University of Massachusetts - Amherst
  • A Saxena
  • DJ Frantzeskakis
Abstract
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.
Publication Date
June 28, 2010
Publisher Statement
DOI: 10.1016/j.physleta.2010.05.014
Citation Information
Y Shen, F Williams, N Whitaker, PG Kevrekidis, et al.. "On some single-hump solutions of the short-pulse equation and their periodic generalizations" Physics Letters A Vol. 374 Iss. 29 (2010)
Available at: http://works.bepress.com/panos_kevrekidis/196/