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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2008, Number 1, Pages 4–18
(Mi basm1)
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This article is cited in 3 scientific papers (total in 3 papers)
The transvectants and the integrals for Darboux systems of differential equations
V. Baltag, I. Calin Institute of Mathematics and Computer Science, Academy of Sciences of Moldova
Abstract:
We apply the algebraic theory of invariants of differential equations to integrate the polynomial differential systems $dx/dt=P1_(x,y)+xC(x,y)$, $dy/dt=Q1_(x,y)+yC(x,y)$, where real homogeneous polynomials $P_1$ and $Q_1$ have the first degree and $C(x,y)$ is a real homogeneous polynomial of degree $r\ge 1$. In generic cases the invariant algebraic curves and the first integrals for these systems are constructed. The constructed invariant algebraic curves are expressed by comitants and invariants of investigated systems.
Keywords and phrases:
Polynomial differential systems, Darboux integrability, first integrals, invariant algebraic curve, invariant, comitant, transvectant.
Received: 10.01.2008
Citation:
V. Baltag, I. Calin, “The transvectants and the integrals for Darboux systems of differential equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2008, no. 1, 4–18
Linking options:
https://www.mathnet.ru/eng/basm1 https://www.mathnet.ru/eng/basm/y2008/i1/p4
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Abstract page: | 269 | Full-text PDF : | 78 | References: | 57 | First page: | 1 |
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