A remarkable class of non-classical symmetries of the steady two-dimensional boundary-layer equations

We study the steady two-dimensional boundary-layer equations in the flat and axisymmetric case to show that some similarity reductions already found in the literature with ad hoc new methods of reduction are indeed invariant solutions under the action of non-classical symmetries (as introduced by Bluman and Cole). Moreover, we show that the celebrated von Mises transformation that reduces the two-dimensional flat boundary-layer equations to a second-order evolution equation is indeed a Bäcklund transformation related to a non-classical symmetry.