ON FORM-PRESERVING POINT TRANSFORMATION OF PARTIAL-DIFFERENTIAL EQUATIONS

New identities are presented relating arbitrary order partial derivati ves of u(x, t) and u'(x', t') for the general point transformation x' = P(x, t, u), t' = Q(n, t, u), u' = R(x, t, u). These identities are u sed to study the nature of those point transformations which preserve the general form of a wide class of 1 + 1 partial differential equatio ns. These results facilitate the search for point symmetries, both dis crete and continuous (Lie), and assist the search for point transforma tions which reduce equations to canonical, but similar, form. A simple test for the existence of hodograph-type transformations between equa tions of similar form is given.