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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.

MSC:

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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