Localized modes of large amplitudes in nonlinear lattices are considered. Theapplied method allows the reduction of nonlinear problem to a linear inverseproblem of phonons scattering on a local potential. The method is efficient inthe case of strongly localized modes. Analytical description of such modes inmonatomic chain is given. Results of numerical calculations of anharmonic localvibrations of light ions in pure and impure alkali halide crystal arepresented. It is found that, in the case of amplitudes ~0.5A, the vibrationsdepend very strongly on the crystallographic directions.
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