Kinks in higher-order polynomial models

The Symmetries and the General Harmonic Solution to Equations of Maxwell Electrodynamics with an Axion

“…The constructed dual image of a dilaton kink (antikink) is of interest in the context of studying dilaton-axion worlds on a brane and domain walls [11], as well as the decay of a false dilatonaxion vacuum [12] and a number of other studies in the corresponding applications of classical and quantum field theory. Other recently constructed kink-like exact solutions can be found, for example, in [13], [14].…”

A General Harmonic Solution in Dilaton Electrodynamics: An Exact Expression for the Fields and the Generalized Lorentz Force

“…The methods developed in this article can be applied to construct soliton solutions in dilaton-Maxwell electrodynamics (see [9]) with an appropriately selected potential. Interesting results related to the construction and study of kink-type solitons in other theories can be found, for example, in [10], [11].…”

Integration theory for kinks and sphalerons in one dimension

“…We call this type of kink semi-BPS. The Bogomolny argument still works, and there is a kink connecting ϕ − and ϕ + whose energy is given by the formula (16). However, the field equation is more difficult to solve, because the differential ( 7) is only properly defined on Σ.…”

“…Here, V(ϕ) = (1 − ϕ 2 ) 2 so W(ϕ) = ϕ − 2 3 ϕ 3 + 1 5 ϕ 5 . The kink connecting −1 to 1 therefore has energy E = W(1) − W(−1) = 16 15 . The field equation has the solution…”

“…It is important to distinguish double zeros of U from zeros of higher, even multiplicity. Lohe [11], and more recently Khare et al [12], Bazeia et al [13], and Gani and collaborators [14][15][16] have drawn attention to several examples.…”