arXiv subjects
Publications and source records attributed to Ł. T. Stȩpień.
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 derived.
Some new classes of exact solutions (so-called functionally-invariant solutions) of the elliptic and hyperbolic complex Monge-Amp$\grave{e}$re equations and of the second heavenly equation, mixed heavenly equation, asymmetric heavenly equation, evolution form of second heavenly equation, general heavenly equation, real general heavenly equation and one of the real sections of general heavenly equation, are found. Besides non-invariance of these found classes of solutions has been investigated. These classes of solutions determine the new classes of metrics without Killing vectors. A criterion of non-invariance of the solutions belonging to found classes, has been also formulated.
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 bounds are saturated if corresponding Bogomolny equations, different for each submodel, are obeyed.
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 conditions, which must be satisfied by the potentials, for each of these mentioned models, are also derived.
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.