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

R. Ramírez; N. Sadovskaia

paper

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

arXiv:1106.2563

Abstract

In this paper we study the differential equations in $D \subseteq R^{2 N}$ 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.