Kinks and double-kinks in generalized $\phi^{4}$-and $\phi^{8}$-models

TL;DR

This paper explores kink and double-kink solutions in generalized $\

Contribution

It introduces non-polynomial hyperbolic functions to generate novel BPS solutions in $\

Findings

Identification of conditions for minimal energy solutions

Development of models with hyperbolic sine and cosine functions

Discovery of genuine double-kink configurations

Abstract

Examining the $\phi^{4}$ and $\phi^{8}$ 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 $\phi=0$, facilitating the emergence of genuine double-kink-type configurations. Conversely, the second promotes the rise of kink-type solutions.