Jg. Kingston et C. Sophocleous, ON FORM-PRESERVING POINT TRANSFORMATION OF PARTIAL-DIFFERENTIAL EQUATIONS, Journal of physics. A, mathematical and general, 31(6), 1998, pp. 1597-1619
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.