Group classification of a generalized Lane-Emden system. (English) Zbl 1271.34042

The generalized Lane-Emden system is given by \[ \begin{aligned} &xu^{\prime \prime}(x)+nu^{\prime}+xH(v)=0,\\ &xv^{\prime \prime}(x)+nv^{\prime}+xG(u)=0\end{aligned} \] and arises in the modeling of several physical phenomena. The present paper provides a Lie group classification of these systems by determining the associated principal Lie algebra.


34C14 Symmetries, invariants of ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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