PT-symmetry in quasi-integrable models

We reinforce the observations of almost stable scattering in nonintegrable models and show that $\mathcal{P}\mathcal{T}$-symmetry can be used as a guiding principle to select relevant systems also when it comes to integrability properties. We show that the presence of unbroken $\mathcal{P}\mathcal{T}$-symmetry in classical field theories produces quasi-integrable excitations with asymptotically conserved charges.