The intrinsic localized modes in a homogeneous nonlinear one-dimensional lattice are investigated by use of the method of multiple scales combined with a quasidiscreteness approximation. It is shown that, in the presence of cubic anharmonicity, some asymmetric intrinsic localized modes with zero-group velocity can exist in the lattice and that the eigenfrequencies of these localized modes are above the top of the harmonic frequency band.
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