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 in | Physics letters. A Vol. 374; no. 29; pp. 2964 - 2967 |
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| Main Authors | , , , , , |
| Format | Journal Article |
| Language | English |
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Elsevier B.V
28.06.2010
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| 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. |
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| AbstractList | 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. |
| Author | Shen, Y. Williams, F. Whitaker, N. Frantzeskakis, D.J. Kevrekidis, P.G. Saxena, A. |
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| Cites_doi | 10.1016/j.physd.2004.04.007 10.4310/DPDE.2009.v6.n4.a1 10.1103/PhysRevE.64.026613 10.1007/BF03024701 10.1007/s10884-009-9147-4 10.1143/JPSJ.74.239 10.1063/1.2146189 10.1088/0305-4470/39/22/L03 10.1103/PhysRevB.73.024513 10.1103/PhysRevE.80.036603 10.1016/j.physleta.2010.01.004 10.1088/1751-8113/43/8/085203 10.1103/PhysRevE.70.057603 10.1088/0951-7715/18/3/021 |
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| Title | On some single-hump solutions of the short-pulse equation and their periodic generalizations |
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