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We investigate the emergence of singular solutions in a non-local model for amagnetic system. We study a modified Gilbert-type equation for themagnetization vector and find that the evolution depends strongly on the lengthscales of the non-local effects. We pass to a coupled density-magnetizationmodel and perform a linear stability analysis, noting the effect of the lengthscales of non-locality on the system's stability properties. We carry outnumerical simulations of the coupled system and find that singular solutionsemerge from smooth initial data. The singular solutions represent a collectionof interacting particles (clumpons). By restricting ourselves to thetwo-clumpon case, we are reduced to a two-dimensional dynamical system that isreadily analyzed, and thus we classify the different clumpon interactionspossible.

Emergent singular solutions of non-local density-magnetization equations in one dimension