Abstract
Interactions between magnetoplasmons are found for a two-dimensional electron gas with filled Landau levels, in analogy to the phonon-phonon interactions in liquid $^{4}\mathrm{He}$. This interaction lowers the magnetoplasmon excitation energies, so that the magnetoroton mode lies close to or even below the cyclotron resonance energy. The calculations show that such interactions must be taken into account in the study of the inter-Landau-level excitations.
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