Kinks and double-kinks in generalized $\ddot{I}{•}^4$-and $\ddot{I}{•}^8$-models

Abstract

Examining the $\ddot{I}{•}^4$ and $\ddot{I}{•}^8$ models within a two-dimensional framework in the flat spacetime and embracing a theory with unconventional kinetic terms, one investigates the emergence of kinks/antikinks and double-kinks/antikinks. We devote our study to obtaining the field configurations with minimal energy, i.e., solutions possessing a Bogomol'nyi-Prasad-Sommerfield's bound. Next, to accomplish our goal, we adopt non-polynomial generalizing functions, namely, hyperbolic sine and cosine functions: the first produce BPS potentials exhibiting a minimum at $\ddot{I}•=0$, facilitating the emergence of genuine double-kink-type configurations. Conversely, the second promotes the rise of kink-type solutions.

22 pages, 12 captioned figures. To match the version accepted in European Physical Journal C