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Second prolongation of a Lie point symmetry

For

V = ξ^{i} \partial_{x_{i}} + η \partial_{u}

, the second prolongation adds coefficients for

u_{i}

and

u_{ij}

obtained by total differentiation:

η_{i} = D_{i} η - u_{j} D_{i} ξ^{j}, η_{ij} = D_{j} η_{i} - u_{ik} D_{j} ξ^{k} .

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