New twinlike models for scalar fields

TL;DR

This paper explores twinlike scalar field models supporting identical energy densities and stability, deriving conditions for their equivalence and analyzing their linear stability to identify when they share the same fluctuation behavior.

Contribution

It introduces the first order equations compatible with equations of motion for twinlike models and establishes conditions for their twinlike and stability properties.

Findings

Derived first order equations for twinlike models

Identified conditions for twinlike energy density and stability

Showed stability can be preserved with additional constraints

Abstract

This work investigates twinlike scalar field models that support kinks with the same energy density and stability. We find the first order equations compatible with the equations of motion. We use them to calculate the conditions under which they attain the twinlike character. The linear stability is also investigated, and there we show that the addition of extra requirements may lead to the same stability under small fluctuations.