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Lie point symmetry

Prolongation of a Lie point symmetry

For $V=\xi^i\partial_{x_i}+\eta\partial_u$, the second prolongation adds coefficients for $u_i$ and $u_{ij}$ obtained by total differentiation:
$$
\eta_i=D_i\eta-u_jD_i\xi^j,
\qquad
\eta_{ij}=D_j\eta_i-u_{ik}D_j\xi^k.
$$


Second prolongation of a Lie point symmetry

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 32E / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 32E / b / Solution

Second prolongation of a Lie point symmetry

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Second prolongation of a Lie point symmetry

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