Integrable Twelve-Component Nonlinear Dynamical System on a Quasi-One-Dimensional Lattice
Bearing in mind the potential physical applicability of multicomponent completely integrable nonlinear dynamical models on quasi-one-dimensional lattices, we have developed the novel twelve-component and six-component semi-discrete nonlinear integrable systems in the framework of the semi-discrete A...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/214195 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Integrable Twelve-Component Nonlinear Dynamical System on a Quasi-One-Dimensional Lattice. Oleksiy O. Vakhnenko and Vyacheslav O. Vakhnenko. SIGMA 21 (2025), 089, 17 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862731477104459776 |
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| author | Vakhnenko, Oleksiy O. Vakhnenko, Vyacheslav O. |
| author_facet | Vakhnenko, Oleksiy O. Vakhnenko, Vyacheslav O. |
| citation_txt | Integrable Twelve-Component Nonlinear Dynamical System on a Quasi-One-Dimensional Lattice. Oleksiy O. Vakhnenko and Vyacheslav O. Vakhnenko. SIGMA 21 (2025), 089, 17 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Bearing in mind the potential physical applicability of multicomponent completely integrable nonlinear dynamical models on quasi-one-dimensional lattices, we have developed the novel twelve-component and six-component semi-discrete nonlinear integrable systems in the framework of the semi-discrete Ablowitz-Kaup-Newell-Segur scheme. The set of lowest local conservation laws found by the generalized direct recurrent technique was shown to be an indispensable constructive tool in the reduction procedure from the prototype to actual field variables. Two types of admissible symmetries for the twelve-component system and one type of symmetry for the six-component system have been established. The mathematical structure of the total local current was shown to support the charge transportation only by four of six subsystems incorporated into the twelve-component system under study. The twelve-component system is able to model the actions of external parametric drive and external uniform magnetic field via time dependencies and phase factors of coupling parameters.
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| first_indexed | 2026-03-21T19:10:17Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-214195 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T19:10:17Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Vakhnenko, Oleksiy O. Vakhnenko, Vyacheslav O. 2026-02-20T08:00:37Z 2025 Integrable Twelve-Component Nonlinear Dynamical System on a Quasi-One-Dimensional Lattice. Oleksiy O. Vakhnenko and Vyacheslav O. Vakhnenko. SIGMA 21 (2025), 089, 17 pages 1815-0659 2020 Mathematics Subject Classification: 39A36; 37K10; 35Q55; 58J70 arXiv:2509.17976 https://nasplib.isofts.kiev.ua/handle/123456789/214195 https://doi.org/10.3842/SIGMA.2025.089 Bearing in mind the potential physical applicability of multicomponent completely integrable nonlinear dynamical models on quasi-one-dimensional lattices, we have developed the novel twelve-component and six-component semi-discrete nonlinear integrable systems in the framework of the semi-discrete Ablowitz-Kaup-Newell-Segur scheme. The set of lowest local conservation laws found by the generalized direct recurrent technique was shown to be an indispensable constructive tool in the reduction procedure from the prototype to actual field variables. Two types of admissible symmetries for the twelve-component system and one type of symmetry for the six-component system have been established. The mathematical structure of the total local current was shown to support the charge transportation only by four of six subsystems incorporated into the twelve-component system under study. The twelve-component system is able to model the actions of external parametric drive and external uniform magnetic field via time dependencies and phase factors of coupling parameters. Oleksiy O. Vakhnenko acknowledges support from the National Academy of Sciences of Ukraine within the Project No 0122U000887. Vyacheslav O. Vakhnenko acknowledges support from the National Academy of Sciences of Ukraine within the Project No 0123U100182. Oleksiy O. Vakhnenko also acknowledges support from the Simons Foundation (USA) under the Grant SFI-PD-Ukraine-00014573. We are grateful to referees for the constructive criticism directed at improving the quality of the presented results. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Integrable Twelve-Component Nonlinear Dynamical System on a Quasi-One-Dimensional Lattice Article published earlier |
| spellingShingle | Integrable Twelve-Component Nonlinear Dynamical System on a Quasi-One-Dimensional Lattice Vakhnenko, Oleksiy O. Vakhnenko, Vyacheslav O. |
| title | Integrable Twelve-Component Nonlinear Dynamical System on a Quasi-One-Dimensional Lattice |
| title_full | Integrable Twelve-Component Nonlinear Dynamical System on a Quasi-One-Dimensional Lattice |
| title_fullStr | Integrable Twelve-Component Nonlinear Dynamical System on a Quasi-One-Dimensional Lattice |
| title_full_unstemmed | Integrable Twelve-Component Nonlinear Dynamical System on a Quasi-One-Dimensional Lattice |
| title_short | Integrable Twelve-Component Nonlinear Dynamical System on a Quasi-One-Dimensional Lattice |
| title_sort | integrable twelve-component nonlinear dynamical system on a quasi-one-dimensional lattice |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214195 |
| work_keys_str_mv | AT vakhnenkooleksiyo integrabletwelvecomponentnonlineardynamicalsystemonaquasionedimensionallattice AT vakhnenkovyacheslavo integrabletwelvecomponentnonlineardynamicalsystemonaquasionedimensionallattice |