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

Abstract

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