# The existence of Bogomolny decomposition for baby Skyrme models

@article{Stpie2012TheEO, title={The existence of Bogomolny decomposition for baby Skyrme models}, author={Ł. T. Stȩpień}, journal={arXiv: Mathematical Physics}, year={2012} }

We derive the Bogomolny decompositions (Bogomolny equations) for: full baby Skyrme model and for its restricted version (so called, pure baby Skyrme model), in (2+0) dimensions, by using so called, concept of strong necessary conditions. It turns out that Bogomolny decomposition can be derived for restricted baby Skyrme model for arbitrary form of the potential term, while for full baby Skyrme model, such derivation is possible only for some class of the potentials.

## 7 Citations

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:…

On Bogomolny equations in generalized gauged baby BPS Skyrme models

- Physics
- 2016

Using the concept of strong necessary conditions (CSNC), we derive Bogomolny equations and BPS bounds for two modifications of the gauged baby BPS Skyrme model: the nonminimal coupling to the gauge…

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 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…

Topological phase transitions in the gauged BPS baby Skyrme model

- Physics
- 2015

A bstractWe demonstrate that the gauged BPS baby Skyrme model with a double vacuum potential allows for phase transitions from a non-solitonic to a solitonic phase, where the latter corresponds to a…

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,…

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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