2007/11/14 by Darryl D. Holm, Lennon Ó Náraigh, Lennon O. Naraigh +1 · 1 citation
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Theoretical and Computational Physics #nlin.AO
paper · pdf · doi:10.1103/physreve.77.036211
19 pages, 13 figures. Submitted to Phys. Rev. E
arxiv created 2007/11/14 · openalex publication_date 2008/03/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the emergence of singular solutions in a nonlocal model for a magnetic system. We study a modified Gilbert-type equation for the magnetization vector and find that the evolution depends strongly on the length scales of the nonlocal effects. We pass to a coupled density-magnetization model and perform a linear stability analysis, noting the effect of the length scales of nonlocality on the system's stability properties. We carry out numerical simulations of the coupled system and find that singular solutions emerge from smooth initial data. The singular solutions represent a collection of interacting particles (clumpons). By restricting ourselves to the two-clumpon case, we are reduced to a two-dimensional dynamical system that is readily analyzed, and thus we classify the different clumpon interactions possible.