Localized states and their stability in an anharmonic medium with a nonlinear defect

A comprehensive analysis of soliton states localized near a plane defect (a defect layer) possessing nonlinear properties is carried out within a quasiclassical approach for different signs of nonlinearity of the medium and different characters of interaction of elementary excitations of the medium with the defect. A quantum interpretation is given to these nonlinear localized modes as a bound state of a large number of elementary excitations. The domains of existence of such states are determined, and their properties are analyzed as a function of the character of interaction of elementary excitations between each other and with the defect. A full analysis of the stability of all the localized states with respect to small perturbations of amplitude and phase is carried out analytically, and the frequency of small oscillations of the state localized on the defect is determined