# Bogomolny equation for the BPS Skyrme model from strong necessary conditions

@article{Stpie2015BogomolnyEF, title={Bogomolny equation for the BPS Skyrme model from strong necessary conditions}, author={Ł. T. Stȩpień}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2015}, volume={49} }

We present a systematic tool for 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.

## 10 Citations

On Bogomolny Equations in the Skyrme Model

- Physics
- 2018

Using the concept of strong necessary conditions (CSNC), we derive a complete decomposition of the minimal Skyrme model into a sum of three coupled BPS submodels with the same topological bound. The…

Bogomolny equations in certain generalized baby BPS Skyrme models

- Physics
- 2017

By using the concept of strong necessary conditions (CSNCs), we derive Bogomolny equations and Bogomol’nyi–Prasad–Sommerfield (BPS) bounds for two certain modifications of the baby BPS Skyrme model:…

Bogomolny equations for the BPS Skyrme models with impurity

- Physics
- 2019

We show that the BPS Skyrme model, as well as its (2+1) dimensional baby version (restricted), can be coupled with an impurity in the BPS preserving manner. The corresponding Bogomolny equations are…

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

- PhysicsPhysical Review D
- 2019

We have shown the existence of self-dual solitons in a type of generalized Chern-Simons baby Skyrme model where the generalized function (depending only in the Skyrme field) is coupled to the…

How to find BPS equations in some submodels of the Skyrme model using the BPS Lagrangian method

- Environmental Science, MathematicsPROCEEDINGS OF THE 4TH INTERNATIONAL SYMPOSIUM ON CURRENT PROGRESS IN MATHEMATICS AND SCIENCES (ISCPMS2018)
- 2019

In this article we employ the BPS Lagrangian method into some submodels from the Skyrme model to obtain their BPS equations. We report that improvements to the original BPS Lagrangian method are…

The first-order Euler-Lagrange equations and some of their uses

- Mathematics
- 2016

A bstractIn many nonlinear field theories, relevant solutions may be found by reducing the order of the original Euler-Lagrange equations, e.g., to first order equations (Bogomolnyi equations,…

Nonlinearity and Topology

- Physics
- 2020

The interplay of nonlinearity and topology results in many novel and emergent properties across a number of physical systems such as chiral magnets, nematic liquid crystals, Bose–Einstein…

3 0 N ov 2 01 9 Cauchy problem and strong necessary conditions

- Mathematics
- 2019

Boundary or initial conditions have been formulated for the solutions of ordinary and partial differential equations created by the strong necessery conditions. keywords: Action integral, strong…

Cauchy problem and strong necessary conditions

- Mathematics
- 2019

Boundary or initial conditions have been formulated for the solutions of ordinary and partial differential equations created by the strong necessery conditions.

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