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}
}
  • Ł. Stȩpień
  • Published 3 December 2015
  • Physics
  • Journal of Physics A: Mathematical and Theoretical
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
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
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
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
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
  • A. N. Atmaja, I. Prasetyo
  • Environmental Science, Mathematics
    PROCEEDINGS 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
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
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
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
Boundary or initial conditions have been formulated for the solutions of ordinary and partial differential equations created by the strong necessery conditions.

References

SHOWING 1-10 OF 79 REFERENCES
The Existence of Bogomolny Decompositions for Gauged $O(3)$ Nonlinear "sigma" Model and for Gauged Baby Skyrme Models
The Bogomolny decompositions (Bogomolny equations) for the gauged baby Skyrme models: restricted and full one, in (2+0)-dimensions, are derived, for some general classes of the potentials. The
Thermodynamics of the BPS Skyrme model
One problem in the application of the Skyrme model to nuclear physics is that it predicts too large a value for the compression modulus of nuclear matter. Here we investigate the thermodynamics of
Bogomol’nyi equations of classical solutions
We review the Bogomol’nyi equations and investigate an alternative route in obtaining it. It can be shown that the known Bogomol’nyi-Prasad-Sommerfield equations can be derived directly from the
Nuclei as near BPS Skyrmions
We study a generalization of the Skyrme model with the inclusion of a sixth-order term and a generalized mass term. We first analyze the model in a regime where the nonlinear {sigma} and Skyrme terms
BPS Skyrme model and baryons at large N c
Within the class of field theories with the field content of the Skyrme model, one submodel can be found which consists of the square of the baryon current and a potential term only. For this
Bogomol'nyi-Prasad-Sommerfield Skyrme model and nuclear binding energies.
TLDR
The classical Bogomol'nyi-Prasad-Sommerfield soliton solutions of the BPS Skyrme model are used together with corrections from the collective coordinate quantization of spin and isospin to calculate nuclear binding energies, finding that the resulting binding energies are already in excellent agreement with their physical values for heavier nuclei.
BPS Skyrme model and nuclear binding energies
We use the classical BPS soliton solutions of the BPS Skyrme model together with corrections from the collective coordinate quantization of spin and isospin, the electrostatic Coulomb energies, and a
The gauged BPS baby Skyrme model
The baby Skyrme model is a well-known nonlinear field theory supporting topological solitons in two space dimensions. In the limit where the term quadratic in derivatives (the "sigma model term")
...
...