Stability in the energy space for chains of solitons of the Landau-Lifshitz equation

André de Laire (1) , Philippe Gravejat (2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 CMLS - Centre de Mathématiques Laurent Schwartz

We prove the orbital stability of sums of solitons for the one-dimensional Landau-Lifshitz equation with an easy-plane anisotropy, under the assumptions that the (non-zero) speeds of the solitons are different, and that their initial positions are sufficiently separated and ordered according to their speeds.

Mots clés: Landau-Lifshitz equation with an easy-plane anisotropy; Stability; chains of solitons; Landau-Lifshitz equation with an easy-plane anisotropy.

Domaines: Equations aux dérivées partielles [math.AP]

André de Laire, Philippe Gravejat. Stability in the energy space for chains of solitons of the Landau-Lifshitz equation. Journal of Differential Equations, 2015, 258 (1), pp.1-80. ⟨10.1016/j.jde.2014.09.003⟩. ⟨hal-00862835v3⟩