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

A. Alonso-Izquierdo, M. A. González León, A. González-Parra, J. Martín-Vaquero

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.

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

Abstract

We perform a systematic study of kink solutions in two-component scalar field theories in 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.
Paper Structure (7 sections, 21 equations, 1 figure)

This paper contains 7 sections, 21 equations, 1 figure.

Table of Contents

  1. Introduction
  2. BPS and semi-BPS kinks in two-component scalar field theories
  3. Models with polynomial superpotentials
  4. Models admitting superpotentials with one singular point
  5. Models admitting superpotentials with two singular points
  6. Confluences between models with different superpotentials
  7. Conclusions

Figures (1)

  • Figure 8: Kink orbits in the $AA$ sector (dark blue), $BB$ sector (light blue) and $AB$ sector (red) for the special cases BNRT $\beta=1$ (left) and BNRT $\beta=1/4$ (right). The black dots represent the vacua in each case.