  We consider the classical integrable structure of two-dimensional non-linear
sigma models with target space three-dimensional Schrodinger spacetimes. There
are the two descriptions to describe the classical dynamics: 1) the left
description based on SL(2,R)_L and 2) the right description based on U(1)_R. We
have shown the sl(2,R)_L Yangian and q-deformed Poincare algebras associated
with them. We proceed to argue an infinite-dimensional extension of the
q-deformed Poincare algebra. The corresponding charges are constructed by using
a non-local map from the flat conserved currents related to the Yangian. The
exotic tower structure of the charges is revealed by directly computing the
classical Poisson brackets. Then the monodromy matrices in both descriptions
are shown to be gauge-equivalent via the relation between the spectral
parameters. We also give a simple Riemann sphere interpretation of this
equivalence.
