On the Solutions of Okubo-Type Systems. (9th February 2021)

• Record Type: Journal Article
• Authors: Filipuk, Galina; Lastra, Alberto
• Other Names: Tsionas Efthymios G. Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2021(2021)
• Publication Date: 2021-02-09
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2021/6690201
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : 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).