The anti-localization of non-stationary linear waves and its relation to the localization. The simplest illustrative problem

We introduce a new wave phenomenon, which can be observed in continuum and discrete systems, where trapped mode exists under certain conditions, namely, the anti-localization of non-stationary linear waves. This is zeroing non-localized propagating component wave-field neighbourhood an inclusion. In other words, it tendency for waves to propagate avoiding The caused by destructive interference harmonics involved into representation solution form Fourier integral. associated with from pass-band, whereas localization related due poles inside stop-band. framework simple illustrative problem considered paper, we have demonstrated that all cases excepting boundary domain parameter space occurs. Thus, absence as well together localization. also investigate influence on whole.