We present a Lagrangian description of the SU(2)/U(1) coset model pert
urbed by its first thermal operator. This is the simplest perturbation
that changes sign under Krammers-Wannier duality. The resulting theor
y, which is a two-component generalization of the sine-Gordon model, i
s then taken in Minkowski space. For negative values of the coupling c
onstant g, it is classically equivalent to the O(4) nonlinear sigma mo
del reduced in a certain frame. For g > 0, it describes the relativist
ic motion of vortices in a constant external field. Viewing the classi
cal equations of motion as a zero curvature condition, we obtain recur
sive relations for the infinitely many conservation laws by the abelia
nization method of gauge connections. The higher spin currents are con
structed entirely using an off-critical generalization of the W(infini
ty) generators. We give a geometric interpretation to the correspondin
g charges in terms of embeddings. Applications to the chirally invaria
nt U(2) Gross-Neveu model are also discussed.