 First prolongation

ID: first-prolongation

For

V = ξ (x, u) \partial_{x} + η (x, u) \partial_{u}

, the first prolongation is

pr^{(1)} V = V + [η_{x} + (η_{u} - ξ_{x}) u^{'} - ξ_{u} (u^{'})^{2}] \partial_{u^{'}} .

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