  We study string theory on the pp-wave geometry obtained by taking the Penrose
limit around a certain null geodesic of the non-supersymmetric Schrodinger
background. We solve for the spectrum of bosonic excitations and find
compelling agreement with the dispersion relation of the giant magnons in the
Schrodinger background obtained previously in arXiv:1712.03091. Inspired by the
pp-wave spectrum we conjecture an exact in the t'Hooft coupling dispersion
relation for the magnons in the original Schrodinger background. We show that
the pp-wave background admits exactly 16 Killing spinors. We use the explicit
form of the latter in order to derive the supersymmetry algebra of the
background which explicitly depends on the deformation parameter. Its bosonic
subalgebra is of the Newton-Hooke type.
