On the Solutions of Okubo-Type Systems
We show that for certain systems of Okubo-type, we can find a solution vector, all components of which are expressed in terms of the first one. This first component can be expressed in two ways. It solves a Volterra integral equation with the kernel expressed in terms of the solutions of a reduced O...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6690201 |
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| _version_ | 1832547045075845120 |
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| author | Galina Filipuk Alberto Lastra |
| author_facet | Galina Filipuk Alberto Lastra |
| author_sort | Galina Filipuk |
| collection | DOAJ |
| description | We show that for certain systems of Okubo-type, we can find a solution vector, all components of which are expressed in terms of the first one. This first component can be expressed in two ways. It solves a Volterra integral equation with the kernel expressed in terms of the solutions of a reduced Okubo-type system of smaller dimension. It is also expressed as a power series about the origin with coefficients satisfying certain recurrence relation. This extends the results in (W. Balser, C. Röscheisen, J. Differential Equations, 2009). |
| format | Article |
| id | doaj-art-d982e2bbec9c4be3a1bdc1e460ebe243 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-d982e2bbec9c4be3a1bdc1e460ebe2432025-02-03T06:46:15ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66902016690201On the Solutions of Okubo-Type SystemsGalina Filipuk0Alberto Lastra1University of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Banacha 2, 02–097 Warsaw, PolandUniversity of Alcalá, Departamento de Física y Matemáticas, Ap. de Correos 20, E-28871 Alcalá de Henares (Madrid), SpainWe show that for certain systems of Okubo-type, we can find a solution vector, all components of which are expressed in terms of the first one. This first component can be expressed in two ways. It solves a Volterra integral equation with the kernel expressed in terms of the solutions of a reduced Okubo-type system of smaller dimension. It is also expressed as a power series about the origin with coefficients satisfying certain recurrence relation. This extends the results in (W. Balser, C. Röscheisen, J. Differential Equations, 2009).http://dx.doi.org/10.1155/2021/6690201 |
| spellingShingle | Galina Filipuk Alberto Lastra On the Solutions of Okubo-Type Systems Journal of Mathematics |
| title | On the Solutions of Okubo-Type Systems |
| title_full | On the Solutions of Okubo-Type Systems |
| title_fullStr | On the Solutions of Okubo-Type Systems |
| title_full_unstemmed | On the Solutions of Okubo-Type Systems |
| title_short | On the Solutions of Okubo-Type Systems |
| title_sort | on the solutions of okubo type systems |
| url | http://dx.doi.org/10.1155/2021/6690201 |
| work_keys_str_mv | AT galinafilipuk onthesolutionsofokubotypesystems AT albertolastra onthesolutionsofokubotypesystems |