Stability and oscillations of two-dimensional solitons described by the perturbed nonlinear Schrodinger equation

A perturbation theory for determining the stability characteristics of spat ial optical solitons with a 2D transverse profile in a transparent medium w ith a weak saturation of nonlinear refractive index is developed. For Kerr nonlinearity, a new solution of linearized equations for weak soliton pertu rbations is found. Using this solution, an expression for the stability cha racteristic is deduced, which, in the case of unstable solitons, determines their decay length and, in the case of stable solitons, shows the presence of perturbations with anomalously weak damping (internal modes) and determ ines their oscillation period. (C) 2000 MAIK "Nauka/Interperiodica".