Strong symmetry

In the definition of a symmetry of a DE $\mathscr{S}$ we required that if $\Delta$ is the function such that $\mathscr{S}=\{\Delta=0\}$ and $X^{(n)}$ is the prolongation of (the generator of) the symmetry then

for every $p$ such that $\Delta(p)=0.$

If equation (1) is satisfied for every $p$, the symmetry is called a strong symmetry.

There is a relation between usual symmetries and strong ones, the CDW theorem.

________________________________________

________________________________________

________________________________________

Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es