Deformations of kink tails

Kinks in higher-order polynomial models

“…5. The transformation properties of the kink asymptotics with respect to the deformation procedure have been studied [26,27]. A class of deformation functions has been found that transform the power-law asymptotics into power-law, but it was shown that the speed of the field approaching the vacuum value (the power of the coordinate in the asymptotic expression for the field) can change.…”

Thick branes via higher order field theory models with exponential and power-law tails

“…Furthermore, the equation of motion φ = −∂ Ṽ /∂φ reduces to the first order ordinary differential equation [39,56], given by:…”

“…Recently, solitons in the form of deformed kinks with power-law and exponential tails have become an interesting subject of research with important applications in physics. Currently, the necessary conditions for the existence and stability of kink solutions with power-law tails have been well studied [36][37][38][39][40][41][42][43][44]. These new solutions present new characteristics and properties as compared with standard solitons.…”

“…Thus, one may expect that for the power-law tail kink a large part of the soliton mass is concentrated in the tail [38]. For instance, it has been proven that for any kink with a power-law tail, the stability potential decreases as a function proportional to the square inverse of the spatial position [39]. These new generation of kinks have been produced as deformed solutions via a strictly monotonic deforming function with finite and infinite derivatives.…”

“…These changes, in turn, lead to properties that will affect the interaction of solitons and the force between them. Furthermore, it has been shown that the mass of kink changes, by taking into account the properties of the deforming function [39]. The asymptotic behavior of the kink stability will directly affect the brane dynamics and its properties.…”