  We study effects of Kac-Baker long-range dispersive interaction (LRI) between
particles on kink properties in the discrete sine-Gordon model. We show that
the kink width increases indefinitely as the range of LRI grows only in the
case of strong interparticle coupling. On the contrary, the kink becomes
intrinsically localized if the coupling is under some critical value.
Correspondingly, the Peierls-Nabarro barrier vanishes as the range of LRI
increases for supercritical values of the coupling but remains finite for
subcritical values. We demonstrate that LRI essentially transforms the internal
dynamics of the kinks, specifically creating their internal localized and
quasilocalized modes. We also show that moving kinks radiate plane waves due to
break of the Lorentz invariance by LRI.
