The soliton states localized at a point defects are investigated by using the nonlinear Schrödinger equation for various signs of the nonlinearity and for different types of defects. The quantum interpretation of these nonlinear localized modes is given in terms of bound states of a large number of Bose particles. The dynamic properties and stability of these states for different types of interaction between elementary excitations with one another and with the defect are investigated. The boundaries of the region of existence and stability of “impurity” solitons are determined depending on the “intensity” of the defect, and the frequency of small oscillations of a soliton near the defect is calculated.

Solitonlike excitations with frequencies in the gap of a linear spectrum are considered for a diatomic chain with small mass difference. It is shown that these excitations represent themselves as a complicated combination of solitons of the acoustic and quasioptical branches of the spectrum. The evolution of these solutions is studied in the phase plane and analytical expressions are obtained. The situation is general for systems having two interacting fields with the same nonlinearity but with different dispersion signs.

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A new generalized Frenkel-Kontorova (discrete sine-Gordon) model is proposed which treats a crystal as a set of one-dimensional atomic chains interacting with each other. Here, unlike earlier works, the model does not include the fixed field generated by an external rigid substrate. The two-dimensional version of the model is considered, but the three-dimensional generalization can be easily developed. On the basis of the present interacting atomic chain model a computer simulation of the crowdion (or the anticrowdion) in an anisotropic crystal is made. The calculated results completely agree with analytical results of the elasticity theory.

The well-known Frenkel-Kontorova theoretical model is generalized by including the elastic properties of the three-dimensional medium surrounding the discrete atomic chain considered. The generalized sinuse-Gordon equation (SGE) and the integro-differential equation describing the crowdion in a highly anisotropic crystal are described. The numerical solution of these equations corroborates all the analytical estimates.