The effect of the $\phi^4$ kink's internal mode during scattering on $\mathcal{PT}$-symmetric defect

The effect of the $\phi^4$ kink's internal mode (IM) during the scattering from a $\mathcal{PT}$-symmetric defect is investigated. It is demonstrated that if a $\phi^4$ kink hits the defect from the gain side, a noticeable IM is excited, while for the kink coming from the opposite direction the mode excitation is much weaker. In the case when the kink initially carries IM, the IM amplitude is affected by the defect if the kink moves from the gain side and it is not affected when the kink moves in the opposite direction. A two degree of freedom collective variable model is shown to be capable of reproducing principal findings of the present work.