Minimal energy for the traveling waves of the Landau-Lifshitz equation
Andr\'e de Laire
TL;DR
This paper establishes the existence of a minimal energy threshold for traveling wave solutions of the Landau-Lifshitz equation with easy-plane anisotropy across multiple dimensions, linking harmonic map theory and Gross-Pitaevskii kernels.
Contribution
It introduces the concept of a minimal energy for finite energy traveling waves in the Landau-Lifshitz equation, extending understanding across dimensions two to four.
Findings
Existence of a minimal energy for traveling waves.
Connection between Landau-Lifshitz and Gross-Pitaevskii equations.
Use of harmonic map estimates in the analysis.
Abstract
We consider nontrivial finite energy traveling waves for the Landau-Lifshitz equation with easy-plane anisotropy. Our main result is the existence of a minimal energy for these traveling waves, in dimensions two, three and four. The proof relies on a priori estimates related with the theory of harmonic maps and the connection of the Landau-Lifshitz equation with the kernels appearing in the Gross-Pitaevskii equation.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Photonic Systems · Numerical methods for differential equations