Minimal Energy for the Traveling Waves of the Landau--Lifshitz Equation

DOI10.1137/130909081zbMath1305.35123arXiv1206.4901OpenAlexW2075545121MaRDI QIDQ5415053

André De Laire

Publication date: 9 May 2014

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.4901

zbMATH Keywords

Landau-Lifshitz equationminimal energyharmonic maps.nontrivial finite energy traveling waves

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

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The sine-Gordon regime of the Landau-Lifshitz equation with a strong easy-plane anisotropy ⋮ Recent results for the Landau-Lifshitz equation ⋮ Stability of solitons of the Landau-Lifshitz equation with planar anisotropy ⋮ Asymptotic behavior of the initial-boundary value problem of Landau-Lifshitz-Schrödinger type ⋮ Existence and decay of traveling waves for the nonlocal Gross–Pitaevskii equation ⋮ Stability in the energy space for chains of solitons of the Landau-Lifshitz equation ⋮ On the asymptotic stability in the energy space for multi-solitons of the Landau-Lifshitz equation ⋮ Self-similar shrinkers of the one-dimensional Landau-Lifshitz-Gilbert equation ⋮ Decay estimates for solutions of nonlocal semilinear equations

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