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

  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},
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. 

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

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

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

  • A. N. AtmajaI. Prasetyo
  • Environmental Science, Mathematics
  • 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

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

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

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

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

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

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

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




Using a concept of strong necessary conditions we derive the Bogomolny decomposition for systems of two generalized elliptic and parabolic nonlinear partial differential equations (NPDE) of the

Some aspects of self-duality and generalised BPS theories

A bstractIf a scalar field theory in (1+1) dimensions possesses soliton solutions obeying first order BPS equations, then, in general, it is possible to find an infinite number of related field

The existence of Bogomolny decomposition by means of strong necessary conditions

The concept of strong necessary conditions for the extremum of a functional to exist, has been applied to analyse the existence of the Bogomolny decomposition for a system of two coupled nonlinear

Existence of Dual Equations by Means of Strong Necessary Conditions - Analysis of Integrability of Partial Differential Nonlinear Equations

Abstract A concept of strong necessary conditions for extremum of functional has been applied for analysis an existence of dual equations for a system of two nonlinear Partial Differential Equations

Hamilton-Jacobi approach to non-slow-roll inflation

I describe a general approach to characterizing cosmological inflation outside the standard slow-roll approximation, based on the Hamilton-Jacobi formulation of scalar field dynamics. The basic idea

Exact Classical Solution for the 't Hooft Monopole and the Julia-Zee Dyon

We present an exact solution to the nonlinear field equations which describe a classical excitation possessing magnetic and electric charge. This solution has finite energy and exhibits explicitly

BPS solutions to a generalized Maxwell–Higgs model

We look for topological BPS solutions of an Abelian Maxwell–Higgs theory endowed by non-standard kinetic terms to both gauge and scalar fields. Here, the non-usual dynamics are controlled by two

Algebraic construction of twinlike models

If the generalized dynamics of K field theories (i.e., field theories with a non-standard kinetic term) is taken into account, then the possibility of so-called twin-like models opens up, that is, of

More on Bogomol’nyi equations of three-dimensional generalized Maxwell-Higgs model using on-shell method

A bstractWe use a recent on-shell method, developed in [1], to construct Bogomol’nyi equations of the three-dimensional generalized Maxwell-Higgs model [2]. The resulting Bogomol’nyi equations are