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First integrals for a generalized coupled Lane-Emden system. (English) Zbl 1216.34002
The generalized coupled Lane-Emden system $$\frac{d^2u}{dt^2}+\frac{n}{t}\frac{du}{dt}+f(t)v^q=0,\quad \frac{d^2v}{dt^2}+\frac{n}{t}\frac{dv}{dt}+f(t)u^p=0$$ is considered, where $n,p,q$ are real constants and $f$ is an arbitrary real-valued function. The authors study the complete Noether symmetry classification of this system with respect to the standard first-order Lagrangian. Several cases for the function $f$ which result in Noether point symmetries are obtained. For each case, the authors obtain a first integral for the corresponding Noether operator.

34A05Methods of solution of ODE
34C14Symmetries, invariants (ODE)
Full Text: DOI
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