  In this note we study soliton, breather and shockwave solutions in certain
two dimensional field theories. These include: (i) Heisenberg's model suggested
originally to describe the scattering of high energy nucleons (ii) $T\bar T$
deformations of certain canonical scalar field theories with a potential. We
find explicit soliton solutions of these models with sine-Gordon and Higgs-type
potentials. We prove that the $T\bar T$ deformation of a theory of a given
potential does not correct the mass of the soliton of the undeformed one. We
further conjecture the form of breather solutions of these models. We show that
certain $T\bar T$ deformed actions admit shockwave solutions that generalize
those of Heisenberg's Lagrangian.
