Family of potentials with power law kink tails

We provide examples of a large class of one-dimensional higher-order field theories with kink solutions which asymptotically have a power law tail either at one end or at both ends. In particular, we provide examples of a family of potentials which admit a kink as well as a mirror kink solution where all four ends of the two kinks, or only two extreme ends of the two kinks have a power law tail (while the two ends facing each other have an exponential tail). The remaining case includes the situation when the ends facing each other have a power law tail while the two extreme ends of the two kinks have an exponential tail. Further, we show that for a kink with a power law tail at either one end or at both ends, there is no gap between the zero mode and the continuum of the corresponding stability equation. This is in contrast with the kinks with an exponential tail at both ends, in which case there is always a gap between the zero mode and the continuum.