Dynamics and stability of localized modes in nonlinear media with point defects

The soliton states localized at a point defects are investigated by using the nonlinear Schrodinger 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. (C) 1997 American Institute of Physics.