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arXiv · 1106.2563

Various aspects of differential equations having a complete set of independent first integrals

R. Ramírez·N. Sadovskaia
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Abstract

In this paper we study the differential equations in $D\subseteq \R^{2N}$ having a complete set of independent first integrals. In particular we study the case when the first integrals are \[f_ν=(Ax_ν+By_ν)^2+\displaystyle\sum_{j=1}^{N}\dfrac{(x_νy_j-x_jy_ν)^2}{a_ν-a_j},\]for $ν=1,...,N,$ where $A,B$ and $a_1<a_2...<a_N$ are constants.

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R. Ramírez, N. Sadovskaia. 2011-06-13. Various aspects of differential equations having a complete set of independent first integrals. https://arxiv.org/abs/1106.2563

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