  We deform two-dimensional quantum field theories by antisymmetric
combinations of their conserved currents that generalize Smirnov and
Zamolodchikov's $T\bar{T}$ deformation. We obtain that energy levels on a
circle obey a transport equation analogous to the Burgers equation found in the
$T\bar{T}$ case. This equation relates charges at any value of the deformation
parameter to charges in the presence of a (generalized) Wilson line. We
determine the initial data and solve the transport equations for antisymmetric
combinations of flavor symmetry currents and the stress tensor starting from
conformal field theories. Among the theories we solve is a conformal field
theory deformed by $J\bar{T}$ and $T\bar{T}$ simultaneously. We check our
answer against results from AdS/CFT.
