Giant magnons and spiky strings in the Schrödinger/dipole-deformed CFT correspondence

We construct semi-classical string solutions of the Schrödinger $Sc{h}_5\times S^5$ 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 $Ad{S}_5\times S^5$ 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 $Sc{h}_5$ part of the metric. Finally, we speculate on the form of the dual field theory operators.