  We obtain the Schrodinger and general pp-wave solutions with or without the
massive vector in Einstein-Weyl supergravity. The vector is an auxiliary field
in the off-shell supermultiplet and it acquires a kinetic term in the
Weyl-squared super invariant. We study the supersymmetry of these solutions and
find that turning on the massive vector has a consequence of breaking all the
supersymmetry. The Schrodinger and also the pp-wave solutions with the massive
vector turned off on the other hand preserve 1/4 of the supersymmetry.
