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A theory of stationary anharmonic localized modes in solids with the cubic and hard quartic lattice anharmonicity is formulated. The theory using the lattice-Green's function method is, in principle, applicable to any type of solids, ordered or disordered, of any dimension. Nonlinear eigenvalue problems for a fundamental mode and its higher harmonics are solved in a successive manner. The obtained result is illustrated for a d -dimensional version of the simple cubic lattice with nearest neighbor interactions to obtain concrete results for the localized-mode frequency, its profile functions, lattice distortions, and so on. For extreme localization, the stationary anharmonic localized mode is well described by a generalized anharmonic Einstein oscillator model.
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Shôzô Takeno (1992) studied this question.
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