Asymptotic behavior of radially symmetric self-focused beams

Radially symmetric self-focused beams near solitonlike solutions are studied in the framework of the nonlinear Schrodinger equation for physically relevant nonlinearities. From the numerical solutions, three main types of oscillations are identified, which are characterized by one or more well-defined frequencies and by the presence or lack of the damping associated with radiation emission. Concepts borrowed from linear quantum mechanics are shown to provide many valuable insights into the observed behavior.