  Two-dimensional CFTs and integrable models have an infinite set of conserved
KdV higher spin currents. These currents can be argued to remain conserved
under the $T\bar{T}$ deformation and its generalizations. We determine the flow
equations the KdV charges obey under the $T\bar{T}$ deformation: they behave as
probes "riding the Burgers flow" of the energy eigenvalues. We also study a
Lorentz-breaking $T_{s+1}\bar{T}$ deformation built from a KdV current and the
stress tensor, and find a super-Hagedorn growth of the density of states.
