Nanoscale excitations of solids in the form of axially symmetric solitons

Abstract

Soliton excitations in solids are a development of the traditional concept of exciton-type electronic excitations. Their main feature is the space and, generally speaking, time distributed amplitude. The spatial distribution of the amplitude is of several nanometers (up to 10 nm). It occurs due to the nonlinearity caused by the interaction of excitation with the lattice. New aspects of the cubic nonlinearity are considered. It is known that the nonlinear Schrodinger equation (NSE) with cubic nonlinearity has analytical solutions in the class of hyperbolic functions and only for the spatial-one-dimensional case. It turned out that there is a physically consistent case where it is possible to evenly divide variables in a spatial-three-dimensional NSE in terms of generalized functions, as well as to find and analyze an analytical solution.