Generalized symmetries for P.D.E.'s of the form u_t=f(u)u_xxx and u_t=D_x³(f(u))
by
David Pidgeon
Massey University

The expansion and solving of the generalised symmetry condition {D_H(Q)=0}_H[u]=0 for H[u]={u_t-f(u)u_xxx=0} and H[u]={u_t-D_x³(f(u))=0} for a symmetry characteristic Q[u] of the fifth order leads to a unique form of the symmetry characteristic for the two types of P.D.E. and two O.D.E.s in the undetermined function f(u). Solving these two O.D.E.s has proved to be elusive; however, by exploiting the point symmetries of these O.D.Es, particular solutions can be found, one of which leads to the well known Harry Dym equation.

Date received: October 23, 2000