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Zooming in: From spatially extended traveling waves to localized structures: The case of the Sine-Gordon equation in (1+3) dimensions
The Sine-Gordon equation in (1+3) dimensions has N-traveling front (“kink”, “domain wall”)- solutions for all N ≥ 1. A nonlinear functional of the solution, which vanishes on a single-front, maps multi-front solutions onto sets of infinitely long, but laterally bounded, rods, which move in space. Ea...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Public Library of Science
2017
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5397037/ https://www.ncbi.nlm.nih.gov/pubmed/28422999 http://dx.doi.org/10.1371/journal.pone.0175783 |
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author | Zarmi, Yair |
author_facet | Zarmi, Yair |
author_sort | Zarmi, Yair |
collection | PubMed |
description | The Sine-Gordon equation in (1+3) dimensions has N-traveling front (“kink”, “domain wall”)- solutions for all N ≥ 1. A nonlinear functional of the solution, which vanishes on a single-front, maps multi-front solutions onto sets of infinitely long, but laterally bounded, rods, which move in space. Each rod is localized in the vicinity of the intersection of two Sine-Gordon fronts. The rod systems are solutions of the linear wave equation, driven by a term that is constructed out of Sine-Gordon fronts. An additional linear operation maps multi-rod systems onto sets of blobs. Each blob is localized in the vicinity of rod intersection, and moves in space. The blob systems are solutions of the linear wave equation, driven by a term that is also constructed out of Sine-Gordon fronts. The temporal evolution of multi-blob solutions mimics elastic collisions of systems of spatially extended particles. |
format | Online Article Text |
id | pubmed-5397037 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2017 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-53970372017-05-04 Zooming in: From spatially extended traveling waves to localized structures: The case of the Sine-Gordon equation in (1+3) dimensions Zarmi, Yair PLoS One Research Article The Sine-Gordon equation in (1+3) dimensions has N-traveling front (“kink”, “domain wall”)- solutions for all N ≥ 1. A nonlinear functional of the solution, which vanishes on a single-front, maps multi-front solutions onto sets of infinitely long, but laterally bounded, rods, which move in space. Each rod is localized in the vicinity of the intersection of two Sine-Gordon fronts. The rod systems are solutions of the linear wave equation, driven by a term that is constructed out of Sine-Gordon fronts. An additional linear operation maps multi-rod systems onto sets of blobs. Each blob is localized in the vicinity of rod intersection, and moves in space. The blob systems are solutions of the linear wave equation, driven by a term that is also constructed out of Sine-Gordon fronts. The temporal evolution of multi-blob solutions mimics elastic collisions of systems of spatially extended particles. Public Library of Science 2017-04-19 /pmc/articles/PMC5397037/ /pubmed/28422999 http://dx.doi.org/10.1371/journal.pone.0175783 Text en © 2017 Yair Zarmi http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. |
spellingShingle | Research Article Zarmi, Yair Zooming in: From spatially extended traveling waves to localized structures: The case of the Sine-Gordon equation in (1+3) dimensions |
title | Zooming in: From spatially extended traveling waves to localized structures: The case of the Sine-Gordon equation in (1+3) dimensions |
title_full | Zooming in: From spatially extended traveling waves to localized structures: The case of the Sine-Gordon equation in (1+3) dimensions |
title_fullStr | Zooming in: From spatially extended traveling waves to localized structures: The case of the Sine-Gordon equation in (1+3) dimensions |
title_full_unstemmed | Zooming in: From spatially extended traveling waves to localized structures: The case of the Sine-Gordon equation in (1+3) dimensions |
title_short | Zooming in: From spatially extended traveling waves to localized structures: The case of the Sine-Gordon equation in (1+3) dimensions |
title_sort | zooming in: from spatially extended traveling waves to localized structures: the case of the sine-gordon equation in (1+3) dimensions |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5397037/ https://www.ncbi.nlm.nih.gov/pubmed/28422999 http://dx.doi.org/10.1371/journal.pone.0175783 |
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