Is a particular case of the generalized symmetry of an ODE. In this case
$$ Y=\xi(x,u) \partial x+\eta (x,u) \partial u + \sum_{i=1}^{m-1} \eta^{i}(x, u^{(m-1)}) \partial u_i $$where $\xi,\eta \in \mathcal{C}^{\infty}(\mathbb{R}^2)$, and $\eta^{i}$ satisfies the same prolongation formula than generalized symmetries:
$$ \eta^{i}(x, u^{(m-1)})=A(\eta^{i-1})-A (\xi) \cdot u_i. $$Is the 1-dimensional case of a symmetry group of a DE system.
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Author of the notes: Antonio J. Pan-Collantes
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