Probability of breaking of the $\mathcal{PT}$ symmetry at collision between breathers with random phases in the model of a $\mathcal{PT}$ symmetric planar coupler

The interaction between breathers has been studied in the model of a nonlinear plane $\mathcal{PT}$-symmetric coupler. It has been shown that the dynamics of the interaction depends significantly on the relative phase of the breathers. The probability of breaking of the $\mathcal{PT}$ symmetry in the collision of breathers having random initial phases has been estimated for various sets of parameters of the model and breathers. Various scenarios of collision of breathers have been described.