Academic Editor: G. Rega
Copyright © 2011 R. Naz et al. This is an open access article distributed under the
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We investigate Noether and partial Noether operators of point type corresponding to a Lagrangian and a partial Lagrangian for a system of two linearly coupled
nonlinear Duffing oscillators. Then, the first integrals with respect to Noether
and partial Noether operators of point type are obtained explicitly by utilizing Noether and partial Noether theorems for the system under consideration.
Moreover, if the partial Euler-Lagrange equations are independent of derivatives, then the partial Noether operators become Noether point symmetry generators
for such equations. The difference arises in the gauge terms due to Lagrangians
being different for respective approaches. This study points to new ways of constructing first integrals for nonlinear equations without regard to a Lagrangian.
We have illustrated it here for nonlinear Duffing oscillators.