Impurity modes in a curved Fermi–Pasta–Ulam chain

The spatial localization properties of nonlinear excitations/modes supported by a curved Fermi–Pasta–Ulam (FPU) lattice chain in presence of an isolated impurity of mass lighter or heavier than the host mass, is investigated. The impurity modes oscillate locally at and around the impurity site. It is examined that a light-mass impurity mode fulfills non-resonance with the linear (or phonon) spectrum because its frequency is located above the phonon band whereas frequency of a heavy-mass impurity mode drops into the phonon band. The phenomenon of resonance of impurities with plane waves explains the lifetimes of localized impurity modes in the nonlinear system.