  We construct semi-classical string solutions of the Schr\"odinger $Sch_5
\times S^5$ spacetime, which is conjectured to be the gravity dual of a
non-local dipole-deformed CFT. They are the counterparts of the giant magnon
and spiky string solutions of the undeformed $AdS_5 \times S^5$ to which they
flow when the deformation parameter is turned off. They live in an $S^3$
subspace of the five-sphere along the directions of which the $B$-field has
non-zero components having also extent in the $Sch_5$ part of the metric.
Finally, we speculate on the form of the dual field theory operators.
