Prolongation of a Lie point symmetry

The prolongation of a point-symmetry generator is its induced vector field on derivatives of the dependent variable. A generator is a symmetry of a differential equation

F = 0

when its required prolongation sends

F

to zero on the solution manifold.

Table of contents
- Second prolongation of a Lie point symmetry Prolongation of a Lie point symmetry

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} .

 Ancestors (6)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version