We show that parity-time- ($\mathcal{PT}$-) symmetric coupled optical waveguides with gain and loss support localized oscillatory structures similar to the breathers of the classical ${\varphi }^4$ model. The power carried by the $\mathcal{P}\mathcal{T}$ breather oscillates periodically, switching back and forth between the waveguides, so that the gain and loss are compensated on the average. The breathers are found to coexist with solitons and to be prevalent in the products of the soliton collisions. We demonstrate that the evolution of a small-amplitude breather's envelope is governed by a system of two coupled nonlinear Schrödinger equations and employ this Hamiltonian system to show that small-amplitude $\mathcal{P}\mathcal{T}$ breathers are stable.

• Received 10 September 2012

DOI:https://doi.org/10.1103/PhysRevA.86.053809