The Born-Infeld vortices induced from a generalized Higgs mechanism.
We construct self-dual Born-Infeld vortices induced from a generalized Higgs mechanism. Two specific models of the theory are of focused interest where the Higgs potential is either of a |ϕ|4- or |ϕ|6-type. For the |ϕ|4-model, we obtain a sharp existence and uniqueness theorem for doubly periodic and planar vortices. For doubly periodic solutions, a necessary and sufficient condition for the existence is explicitly derived in terms of the vortex number, the Born-Infeld parameter, and the size of the periodic lattice domain. For the |ϕ|6-model, we show that both topological and non-topological vortices are present. This new phenomenon distinguishes the model from the classical Born-Infeld-Higgs theory studied earlier in the literature. A series of results regarding doubly periodic, topological, and non-topological vortices in the |ϕ|6-model are also established.
Institute of Contemporary Mathematics, School of Mathematics and Statistics, Henan University , Kaifeng, Henan 475004, People's Republic of China.
Xiaosen
0000-0001-7665-8421
X
Han
Born–Infeld electromagnetism; Higgs mechanism; gauge fields; nonlinear elliptic equations; self-dual vortex equations