The First-Order Euler-Lagrange equations and some of their uses

Abstract

In 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.

arXiv commentLatex, 29 pages

References in corpus (19)

• A Skyrme-type proposal for baryonic matter
• Generalized Global Defect Solutions
• Hidden supersymmetry of domain walls and cosmologies
• Braneworld Models of Scalar Fields with Generalized Dynamics
• First-order formalism and dark energy
• First-order framework and generalized global defect solutions
• k-defects as compactons
• BPS Skyrmions as neutron stars
• Some aspects of self-duality and generalised BPS theories
• Kinks in a non-linear massive sigma model
• BPS Solutions to a Generalized Maxwell-Higgs Model
• First-order framework and domain-wall/brane-cosmology correspondence
• $\delta N$ formalism from superpotential and holography
• Hairy black holes in the general Skyrme model
• Black hole Skyrmion in a generalized Skyrme model
• First-order formalism for dark energy and dust
• A Detailed Study of Bogomol'nyi Equations in Two-Dimensional Generalized Maxwell-Higgs Model Using \textit{On-Shell} Method
• Solitons on tori and soliton crystals
• The existence of Bogomolny decompositions for gauged baby Skyrme models

Cited by in corpus (12)

• The ${\varphi }^4$ model with the BPS preserving defect
• BPS soliton-impurity models and supersymmetry
• Non-topological kink scattering in a two-component scalar field theory model
• The BPS property and its breaking in 1+1 dimensions
• Radially symmetric scalar solitons
• Exact self-duality in a modified Skyrme model
• Self-dual sectors for scalar field theories in (1 + 1) dimensions
• Inflationary Twin Models
• Some Comments on BPS systems
• Bogomolny equations for the BPS Skyrme models with impurity
• Bogomol'nyi equations for Dirac-Born-Infeld cosmic string
• Examples for BPS solitons destabilized by quantum effects