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

Abstract Examining the $$\phi ^{4}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math> and $$\phi ^{8}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mn>8</mml:mn> </mml:msup> </mml:math> 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 $$\phi =0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , facilitating the emergence of genuine double-kink-type configurations. Conversely, the second promotes the rise of kink-type solutions.