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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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Autor principal: Zarmi, Yair
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2017
Materias:
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
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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.
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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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