Bogomolny equation for the BPS Skyrme model from strong necessary conditions

Abstract

We present a systematic tool of derivation of the Bogomolny equation for the BPS Skyrme model. Furthermore, we find a generalization of the Bogomolny equation to the case corresponding with a non-zero value of the external pressure. The method is based on the concept of strong necessary conditions and can be applied to any Skyrme like theory.

Bogomolny equations for the BPS Skyrme models with impurity

“…The derivation of Bogomolny equations for some field theory systems in lower dimension, by using the CSNC method, was presented in [43,45,[48][49][50]. It was also applied to baby Skyrme theories and their gauged version, in [8] and [9], correspondingly.…”

The Bogomolny Decomposition for Systems of Two Generalized Nonlinear Partial Differential Equations of the Second Order

“…In 1979 the first attempt to combine both the Rund and the Bogomolny methods has been done [11]. During the two last decades these results have been improved and generalized [12][13][14][15][16][17]. The developed formalism named the strong necessary conditions method (SNCM), uniquely treats the Rund and the Bogomolny approaches.…”

“…We consider so called generalized systems of nonlinear partial differential equations with coefficients dependent on unknown functions [16].…”

Self-dual solitons in a Maxwell-Chern-Simons baby Skyrme model

“…Thus, BPS solitons has been obtained in a gauged restricted model whose gauge field dynamics is governed by the Maxwell term [41]. All these results have inspired the development a wide range of applications, including topological phase transitions [30], Bogomol'nyi equations based in the strong necessary conditions limit [42], gauged BPS baby skyrmions with quantized magnetic flux [43] and even in supersymmetry [44][45][46][47][48] and gravitational theories [49].…”