On some single-hump solutions of the short-pulse equation and their periodic generalizations
Publication Date
2010
Journal or Book Title
PHYSICS LETTERS A
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.
Pages
2964-2967
Volume
374
Issue
29
Recommended Citation
Shen, Y; Williams, F; Whitaker, N; Kevrekidis, PG; Saxena, A; and Frantzeskakis, DJ, "On some single-hump solutions of the short-pulse equation and their periodic generalizations" (2010). PHYSICS LETTERS A. 19.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/19
Comments
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