Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 3 / 33A / c

Table of contents
- Solution c

Solution

Let

Δ (x, u, u^{'}) = u^{'} - F (x, u)

. Applying the first prolongation gives

pr^{(1)} V (Δ) = η_{x} + (η_{u} - ξ_{x}) u^{'} - ξ_{u} (u^{'})^{2} - ξ F_{x} - η F_{u} .

On the solution manifold

Δ = 0

, one has

u^{'} = F

. The infinitesimal symmetry criterion is therefore exactly

0 = η_{x} + (η_{u} - ξ_{x} - F ξ_{u}) F - ξ F_{x} - η F_{u} .

 Ancestors (10)

 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