Wide class of logarithmic potentials with power-tower kink tails

Abstract

We present a wide class of potentials which admit kinks and corresponding mirror kinks with either a power law or an exponential tail at the two extreme ends and a power-tower form of tails at the two neighbouring ends, i.e. of the forms ette or pttp where e, p and t denote exponential, power law and power-tower tail, respectively. We analyze kink stability equation in all these cases and show that there is no gap between the zero mode and the beginning of the continuum. Finally, we provide a recipe for obtaining logarithmic potentials with power-tower kink tails and estimate kink-kink interaction strength.

Deformations of kink tails

“…Thus, we conclude that under deformation with a good enough deforming function, the power of the coordinate does not change, but the coefficient A k changes in accordance with Eq. (35).…”

“…This, in turn, leads to a fundamentally new dynamics of such systems, in comparison with the case of exponential asymptotics. It should be noted that kinks with power-law asymptotics also appear in some models with non-polynomial potentials [31][32][33][34][35].…”

Explicit Kink Solutions in Several One-Parameter Family of Higher Order Field Theory Models

“…Another open problem is to enquire if there exist higher order field theory models which have superexponential [21,22], super-super-exponential [23] or power-tower [24] type of tails. One criticism against the models presented in Sec.…”

“…Beyond sine-Gordon [17], the latter include double sine-Gordon [19] and Lamé [20] solitons as examples. Further, recently explicit kink solutions with super-exponential [21,22] and super-super-exponential [23], power-tower [24] as well as power-law tail [25,26,27,28,29] have also been obtained. Thus, it is of immense interest to obtain explicit kink solutions in as many higher order field theory models as possible.…”

Exotic final states in the $$\varphi ^8$$ multi-kink collisions

“…Interestingly, the variety of asymptotic behaviors of kinks is not limited to exponential and power-law ones. In some models, kink solutions have super-exponential [19,20] and power-tower [21] asymptotics. In addition, it is possible to construct so-called compact kinks that have no tails at all, i.e., have a compact support, see, e.g., [22,23] and references therein.…”