BPS and semi-BPS kink families in two-component scalar field theories with fourth-degree polynomial potentials

TL;DR

This paper systematically studies kink solutions in two-component scalar field theories with quartic potentials, identifying new models that support continuous families of complex, composite kinks with internal structure.

Contribution

It introduces a method to construct and analyze new two-component scalar field models with quartic interactions using the Bogomolny formalism, revealing novel kink families with internal structure.

Findings

Identified new models supporting continuous families of kinks.

Discovered kinks with nontrivial internal structure and composite configurations.

Extended the class of known solutions in two-component scalar field theories.

Abstract

We perform a systematic study of kink solutions in two-component scalar field theories in $(1+1)$ dimensions with interaction terms of at most quartic order. Our approach is based on the Bogomolny formalism, constructing scalar potentials from suitable superpotentials and analyzing the corresponding first-order equations. While cubic polynomial superpotentials naturally generate quartic interactions, we show that more general functional forms also lead to admissible models within the same class. In this way, we identify new models supporting continuous families of kinks with nontrivial internal structure, such that they can be interpreted as composite configurations formed by multiple localized energy lumps.