On Bogomol'nyi Equations of Classical Solutions

TL;DR

This paper reviews the Bogomol'nyi equations, introduces an alternative derivation method from Euler-Lagrange equations, and applies it to Dirac-Born-Infeld solitons to find first-order equations and potentials.

Contribution

It presents a new approach to derive Bogomol'nyi equations directly from Euler-Lagrange equations, bypassing the Hamiltonian, and applies it to noncanonical defects.

Findings

Derived BPS equations from Euler-Lagrange equations

Applied method to Dirac-Born-Infeld solitons

Identified potentials for noncanonical defects

Abstract

We review the Bogomol'nyi equations and investigate an alternative route in obtaining it. It can be shown that the known BPS equations can be derived directly from the corresponding Euler-Lagrange equations via separation of variables, without having to appeal to the Hamiltonian. We apply this technique to the Dirac-Born-Infeld solitons and obtained the corresponding equations and the potentials. This method is suitable for obtaining the first-order equations and determining the allowed potentials for noncanonical defects.