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

@article{Adam2016TheFE, title={The first-order Euler-Lagrange equations and some of their uses}, author={Christoph Adam and Fidel Santamar{\'i}a}, journal={Journal of High Energy Physics}, year={2016}, volume={2016}, pages={1-32} }

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, self-duality equations, etc.). Here we generalise, further develop and apply one particular method for the order reduction of nonlinear field equations which, despite its systematic and versatile character, is not widely known.

## 23 Citations

### Self-dual sectors for scalar field theories in (1 + 1) dimensions

- MathematicsJournal of High Energy Physics
- 2019

A bstractWe use ideas of generalized self-duality conditions to construct real scalar field theories in (1 + 1)-dimensions with exact self dual sectors. The approach is based on a pre-potential U…

### BPS property and its breaking in 1+1 dimensions

- MathematicsPhysical Review D
- 2018

We show that the BPS property is a generic feature of field theories in (1+1) dimensions, which does not put any restriction on the action. Here, by BPS solutions we understand static solutions which…

### 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…

### BPS monopoles and dyons in generalized BPS Lagrangian method

- Physics
- 2021

We generalize BPS Lagrangian method and rederive BPS equations for monopoles and dyons from the Lagrangian of SU(2) Maxwell-Higgs model in four dimensional spacetime. We show that in the BPS…

### Radially symmetric scalar solitons

- Physics, MathematicsPhysical Review D
- 2021

A class of noncanonical effective potentials is introduced allowing stable, radially symmetric, solutions to first order Bogomol’nyi equations for a real scalar field in a fixed spacetime background.…

### Exact self-duality in a modified Skyrme model

- Mathematics
- 2017

A bstractWe propose a modification of the Skyrme model that supports a self-dual sector possessing exact non-trivial finite energy solutions. The action of such a theory possesses the usual quadratic…

### Searching for BPS vortices with nonzero stress tensor in the generalized Born–Infeld–Higgs model

- Physics, Mathematics
- 2018

In this article we show that the new BPS equations for vortices, with nonzero diagonal components of the stress tensor, obtained in \cite{Atmaja:2015lia} for the generalized Maxwell-Higgs model can…

### Searching for BPS Vortex with Nonzero Internal Pressure in Generalized Born-Infeld-Higgs Model

- Physics
- 2018

In this article we show that the BPS equations of vortex with nonzero internal pressure derived in~\cite{Atmaja:2015lia} for the generalized Maxwell-Higgs model can also be obtained using the BPS…

### 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…

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