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 |
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| Date: | 2023 |
| Main Authors: | , , , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2023
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| 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| _version_ | 1862607447573659648 |
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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.
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| first_indexed | 2026-03-14T05:12:16Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211975 |
| 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 |
| record_format | dspace |
| 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. en 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 |
| work_keys_str_mv | AT adamchristoph modulispaceforkinkcollisionswithmovingcenterofmass AT halcrowchris modulispaceforkinkcollisionswithmovingcenterofmass AT oleskatarzyna modulispaceforkinkcollisionswithmovingcenterofmass AT romanczukiewicztomasz modulispaceforkinkcollisionswithmovingcenterofmass AT wereszczynskiandrzej modulispaceforkinkcollisionswithmovingcenterofmass |