Killing spinors and exact plane-wave solutions of extended supergravity

Urrutia's ansatz for exact plane-wave solutions of simple supergravity is generalized to $N=2\mathrm{}$ extended supergravity and conditions are given for the solutions to be nontrivial. Conditions are also given for the plane-wave background to be invariant under a local supersymmetry transformation generated by a Killing spinor. It is seen that even though a bosonic background can admit a spin-$\frac{3}{2}$ solution when it does not possess a Killing spinor, if it is supersymmetric it admits a more general gravitino solution. Comparison is made with the solutions of Aichelburg and Dereli.