Kirr K. Spectral features and stability of nonlinear excitations in molecular nanoclusters and low-dimensional crystals

Object: process of formation of the small amplitude localized nonlinear excitations (analogues of the soliton excitations) in nano sized modulated systems. The goal: establishing of the dynamic and spectral features of the nonlinear excitations and their classification in the molecular nanoclusters and modulated systems of limited size. Methods: algebraic methods of solving of the systems of linear and nonlinear equations, methods of stability of the stationary oscillations, computational modulation of the excitations processes of the nonlinear homogeneous and inhomogeneous oscillations in the molecular nanoclusters and low dimensional crystals. Results: A classification of all types of monochromatic anharmonic oscillations of the discrete modulated nanoclusters is obtained and the analogues of the gap and outgap solitons are carried out, the specialties of their transformation and thermodynamics are obtained. A complex analysis of the nonlinear excitations stability in the modulated crystals is carried out, the conditions and the regions of the stability, and the quantum features of the oscillation instability of such excitations are determined. Field of application: solid state physics