According to AdS/CFT duality semi-classical strings in the Schrödinger spacetime is conjectured to be a holographic dual to dipole CFT. In this paper we consider pulsating strings in five-dimensional Schrödinger space times five-sphere. We have found classical string solutions pulsating entirely in the Schrödinger part of the background. We quantize the theory semi-classically and obtain the wave function of the problem. We have found the corrections to the energy, which by duality are supposed to give anomalous dimensions of certain operators in the dipole CFT. * Emails: h_dimov,rash,vetsov@phys.uni-sofia.bg and miroslavsky@abv.bg

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We find explicit solutions for giant magnons and spiky strings living on the Schrödinger space Schr 5 × T 1,1 and compute dispersion relations. The holographic dual field theory is conjectured to be a non-local dipole-deformed CFT at strong coupling. We find that the dependence between conserved charges in the dispersion relations is transcendental, which is quite different from the most symmetric case of spherical internal space. Keeping the squashing parameter b general allows us to take some limits and to compare our results to known cases.

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