Classical string solutions in Non-Relativistic AdS${}_5\times$S${}^5$: Closed and Twisted sectors

We find classical closed string solutions to the non-relativistic AdS${}_5\times$S${}^5$ string theory which are the analogue of the BMN and GKP solutions for the relativistic theory. We show that non-relativistic AdS${}_5\times$S${}^5$ string theory admits a ${\mathbb{Z}}_2$ orbifold symmetry which allows us to impose twisted boundary conditions. Among the solutions in the twisted sector, we find the one around which the semiclassical expansion in arXiv:2102.00008 takes place.