Self-dual solitons in a Born-Infeld baby Skyrme model

TL;DR

This paper demonstrates the existence of self-dual topological solitons in a gauged Born-Infeld baby Skyrme model, providing analytical bounds and numerical solutions for various soliton profiles.

Contribution

It introduces a novel gauged baby Skyrme model with Born-Infeld dynamics and derives self-dual equations with quantized energy bounds, supported by numerical analysis.

Findings

Existence of three types of self-dual solitons: compacton, Gaussian decay, and power-law decay.

Derivation of a Bogomol'nyi bound proportional to topological charge.

Numerical solutions illustrating different soliton profiles for varying parameters.

Abstract

We show the existence of self-dual (topological) solitons in a gauged version of the baby Skyrme model in which the Born-Infeld term governs the gauge field dynamics. The successful implementation of the Bogomol'nyi-Prasad-Sommerfield formalism provides a lower bound for the energy and the respective self-dual equations whose solutions are the solitons saturating such a limit. The energy lower bound (Bogomol'nyi bound) is proportional to the topological charge of the Skyrme field and therefore quantized. In contrast, the total magnetic flux is a nonquantized quantity. Furthermore, the model supports three types of self-dual solitons profiles: the first describes compacton solitons, the second follows a Gaussian decay law, and the third portrays a power-law decay. Finally, we perform numerical solutions of the self-dual equations and depicted the soliton profiles for different values of the parameters controlling the nonlinearity of the model.