Local amplitude equation from non-local dynamics

2003/01/30 by R. Friedrichs, Rene Friedrichs, A. Engel +3
Biochemistry, Genetics and Molecular Biology · Engineering · Physics and Astronomy · #Characterization and Applications of Magnetic Nanoparticles #FOS: Physical sciences #Geomagnetism and Paleomagnetism Studies #Pattern Formation and Solitons (nlin.PS) #Theoretical and Computational Physics #nlin.PS

paper · pdf · doi:10.48550/arxiv.nlin/0301046

7 pages, 2 figures

arxiv created 2003/01/30 · openalex publication_date 2003/01/30 · arxiv updated 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive a closed equation for the shape of the free surface of a magnetic fluid subject to an external magnetic field. The equation is strongly non-local due to the long range character of the magnetic interaction. We develop a systematic multiple scale perturbation expansion in which the non-locality is reduced to the occurrence of the Hilbert transform of the surface profile. The resulting third order amplitude equation describing the slow modulation of the basic pattern is shown to be purely local.

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