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Spatially Extended Relativistic Particles Out of Traveling Front Solutions of Sine-Gordon Equation in (1+2) Dimensions
Slower-than-light multi-front solutions of the Sine-Gordon in (1+2) dimensions, constructed through the Hirota algorithm, are mapped onto spatially localized structures, which emulate free, spatially extended, massive relativistic particles. A localized structure is an image of the junctions at whic...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Public Library of Science
2016
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4773000/ https://www.ncbi.nlm.nih.gov/pubmed/26930077 http://dx.doi.org/10.1371/journal.pone.0148993 |
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author | Zarmi, Yair |
author_facet | Zarmi, Yair |
author_sort | Zarmi, Yair |
collection | PubMed |
description | Slower-than-light multi-front solutions of the Sine-Gordon in (1+2) dimensions, constructed through the Hirota algorithm, are mapped onto spatially localized structures, which emulate free, spatially extended, massive relativistic particles. A localized structure is an image of the junctions at which the fronts intersect. It propagates together with the multi-front solution at the velocity of the latter. The profile of the localized structure obeys the linear wave equation in (1+2) dimensions, to which a term that represents interaction with a slower-than-light, Sine-Gordon-multi-front solution has been added. This result can be also formulated in terms of a (1+2)-dimensional Lagrangian system, in which the Sine-Gordon and wave equations are coupled. Expanding the Euler-Lagrange equations in powers of the coupling constant, the zero-order part of the solution reproduces the (1+2)-dimensional Sine-Gordon fronts. The first-order part is the spatially localized structure. PACS: 02.30.Ik, 03.65.Pm, 05.45.Yv, 02.30.Ik. |
format | Online Article Text |
id | pubmed-4773000 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2016 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-47730002016-03-07 Spatially Extended Relativistic Particles Out of Traveling Front Solutions of Sine-Gordon Equation in (1+2) Dimensions Zarmi, Yair PLoS One Research Article Slower-than-light multi-front solutions of the Sine-Gordon in (1+2) dimensions, constructed through the Hirota algorithm, are mapped onto spatially localized structures, which emulate free, spatially extended, massive relativistic particles. A localized structure is an image of the junctions at which the fronts intersect. It propagates together with the multi-front solution at the velocity of the latter. The profile of the localized structure obeys the linear wave equation in (1+2) dimensions, to which a term that represents interaction with a slower-than-light, Sine-Gordon-multi-front solution has been added. This result can be also formulated in terms of a (1+2)-dimensional Lagrangian system, in which the Sine-Gordon and wave equations are coupled. Expanding the Euler-Lagrange equations in powers of the coupling constant, the zero-order part of the solution reproduces the (1+2)-dimensional Sine-Gordon fronts. The first-order part is the spatially localized structure. PACS: 02.30.Ik, 03.65.Pm, 05.45.Yv, 02.30.Ik. Public Library of Science 2016-03-01 /pmc/articles/PMC4773000/ /pubmed/26930077 http://dx.doi.org/10.1371/journal.pone.0148993 Text en © 2016 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 Spatially Extended Relativistic Particles Out of Traveling Front Solutions of Sine-Gordon Equation in (1+2) Dimensions |
title | Spatially Extended Relativistic Particles Out of Traveling Front Solutions of Sine-Gordon Equation in (1+2) Dimensions |
title_full | Spatially Extended Relativistic Particles Out of Traveling Front Solutions of Sine-Gordon Equation in (1+2) Dimensions |
title_fullStr | Spatially Extended Relativistic Particles Out of Traveling Front Solutions of Sine-Gordon Equation in (1+2) Dimensions |
title_full_unstemmed | Spatially Extended Relativistic Particles Out of Traveling Front Solutions of Sine-Gordon Equation in (1+2) Dimensions |
title_short | Spatially Extended Relativistic Particles Out of Traveling Front Solutions of Sine-Gordon Equation in (1+2) Dimensions |
title_sort | spatially extended relativistic particles out of traveling front solutions of sine-gordon equation in (1+2) dimensions |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4773000/ https://www.ncbi.nlm.nih.gov/pubmed/26930077 http://dx.doi.org/10.1371/journal.pone.0148993 |
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