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First integrals for a generalized coupled Lane-Emden system. (English) Zbl 1216.34002

The generalized coupled Lane-Emden system

d 2 u dt 2 +n tdu dt+f(t)v q =0,d 2 v dt 2 +n tdv 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)
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