  We show that the (torsional) nonrelativistic string sigma models on $ R\times
S^2 $ can be mapped into \emph{deformed} Rosochatius like integrable models in
one dimension. We also explore the associated Hamiltonian constrained structure
by introducing appropriate Dirac brackets. These results show some solid
evidence of the underlying integrable structure in the nonrelativistic sector
of the gauge/string duality.
