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Multi-dimensional Darboux type differential systems with quadratic nonlinearities

O. V. Diaconescu

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chisinau, Moldova

Abstract: In the article the $n$-dimensional autonomous Darboux type differential systems with nonlinearities of the $2^{nd}$ degree are considered. With the aid of theorem on integrating factor the particular invariant $GL(n, \mathbb R)$-integrals are constructed as well as the first integrals of Darboux type for considered systems. These integrals represent the algebraic curves of the $1^{st}$ degree. The recurrence formula of particular invariant $GL(n,\mathbb R)$-integrals of the Darboux type differential system is found.

Keywords and phrases: The Darboux type differential system, comitant, invariant $GL(n,\mathbb R)$-integrating factor, invariant $GL(n,\mathbb R)$-integral.

MSC: 34C05,34C14

Received: 15.03.2007

Language: English

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