Moduli Space for Kink Collisions with Moving Center of Mass

We apply the collective coordinate model framework to describe collisions of a kink and an antikink with nonzero total momentum, i.e., when the solitons possess different velocities. The minimal moduli space with only two coordinates (the mutual distance and the position of the center of mass) is of...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2023
Main Authors: Adam, Christoph, Halcrow, Chris, Oles, Katarzyna, Romanczukiewicz, Tomasz, Wereszczynski, Andrzej
Format: Article
Language:English
Published: Інститут математики НАН України 2023
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/211975
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Moduli Space for Kink Collisions with Moving Center of Mass. Christoph Adam, Chris Halcrow, Katarzyna Oles, Tomasz Romanczukiewicz and Andrzej Wereszczynski. SIGMA 19 (2023), 054, 18 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Adam, Christoph
Halcrow, Chris
Oles, Katarzyna
Romanczukiewicz, Tomasz
Wereszczynski, Andrzej
author_facet Adam, Christoph
Halcrow, Chris
Oles, Katarzyna
Romanczukiewicz, Tomasz
Wereszczynski, Andrzej
citation_txt Moduli Space for Kink Collisions with Moving Center of Mass. Christoph Adam, Chris Halcrow, Katarzyna Oles, Tomasz Romanczukiewicz and Andrzej Wereszczynski. SIGMA 19 (2023), 054, 18 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We apply the collective coordinate model framework to describe collisions of a kink and an antikink with nonzero total momentum, i.e., when the solitons possess different velocities. The minimal moduli space with only two coordinates (the mutual distance and the position of the center of mass) is of a wormhole type, whose throat shrinks to a point for symmetric kinks. In this case, a singularity is formed. For non-zero momentum, it prohibits solutions where the solitons pass through each other. We show that this unphysical feature can be cured by enlarging the dimension of the moduli space, e.g., by the inclusion of internal modes.
first_indexed 2026-03-14T05:12:16Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-14T05:12:16Z
publishDate 2023
publisher Інститут математики НАН України
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spelling Adam, Christoph
Halcrow, Chris
Oles, Katarzyna
Romanczukiewicz, Tomasz
Wereszczynski, Andrzej
2026-01-20T16:12:46Z
2023
Moduli Space for Kink Collisions with Moving Center of Mass. Christoph Adam, Chris Halcrow, Katarzyna Oles, Tomasz Romanczukiewicz and Andrzej Wereszczynski. SIGMA 19 (2023), 054, 18 pages
1815-0659
2020 Mathematics Subject Classification: 35C08; 35Q51
arXiv:2304.07895
https://nasplib.isofts.kiev.ua/handle/123456789/211975
https://doi.org/10.3842/SIGMA.2023.054
We apply the collective coordinate model framework to describe collisions of a kink and an antikink with nonzero total momentum, i.e., when the solitons possess different velocities. The minimal moduli space with only two coordinates (the mutual distance and the position of the center of mass) is of a wormhole type, whose throat shrinks to a point for symmetric kinks. In this case, a singularity is formed. For non-zero momentum, it prohibits solutions where the solitons pass through each other. We show that this unphysical feature can be cured by enlarging the dimension of the moduli space, e.g., by the inclusion of internal modes.
The authors acknowledge financial support from the Ministry of Education, Culture, and Sports, Spain (Grant No. PID2020-119632GB-I00), the Spanish Consolider-Ingenio 2010 Programme CPAN (CSD2007-00042), the Xunta de Galicia (Grant No. INCITE09.296.035PR and Centro singular de investigaci´on de Galicia accreditation 2019-2022), and the European Union ERDF. C.H. is supported by the Carl Trygger Foundation through the grant CTS 20:25. K.O., T.R., and A.W. were supported by the Polish National Science Centre (Grant No. NCN 2019/35/B/ST2/00059). AW thanks Jose Queiruga for the discussion.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Moduli Space for Kink Collisions with Moving Center of Mass
Article
published earlier
spellingShingle Moduli Space for Kink Collisions with Moving Center of Mass
Adam, Christoph
Halcrow, Chris
Oles, Katarzyna
Romanczukiewicz, Tomasz
Wereszczynski, Andrzej
title Moduli Space for Kink Collisions with Moving Center of Mass
title_full Moduli Space for Kink Collisions with Moving Center of Mass
title_fullStr Moduli Space for Kink Collisions with Moving Center of Mass
title_full_unstemmed Moduli Space for Kink Collisions with Moving Center of Mass
title_short Moduli Space for Kink Collisions with Moving Center of Mass
title_sort moduli space for kink collisions with moving center of mass
url https://nasplib.isofts.kiev.ua/handle/123456789/211975
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AT oleskatarzyna modulispaceforkinkcollisionswithmovingcenterofmass
AT romanczukiewicztomasz modulispaceforkinkcollisionswithmovingcenterofmass
AT wereszczynskiandrzej modulispaceforkinkcollisionswithmovingcenterofmass