3 papers
math.AP2026
Global perturbation of isolated equivariant chiral skyrmions from the Bogomol'nyi case
Slim Ibrahim, Ikkei Shimizu
Isolated skyrmion solutions to the two-dimensional Landau-Lifshitz equation with Dzyaloshinskii-Moriya interaction, Zeeman term, and easy-plane anisotropy of various strengths are…
math.AP2026
Time decay estimates for localized perturbations around a helical state for the Landau-Lifshitz-Gilbert equation
Ikkei Shimizu
We study the dynamics of the Landau--Lifshitz--Gilbert equation with the Dzyaloshinskii--Moriya interaction. The equation admits a family of exact stationary solutions, referred to…
math.AP2025
Phase transition thresholds and chiral magnetic fields of general degree
Slim Ibrahim, Tatsuya Miura, Carlos Román +1
We study a variational problem for the Landau--Lifshitz energy with Dzyaloshinskii--Moriya interactions arising in 2D micromagnetics, focusing on the Bogomol'nyi regime. We first d…