Using the Ehrenfest theorem for determining the self-focusing and self-trapping of nonlinear beams

We discuss how to generalize the Ehrenfest theorem for the computation of the width of nonlinear waves obeying the nonlinear Schrodinger equation. To do that, we model the nonlinear potential as a quantum harmonic oscillator (QHO) whose strength depends on the power and on the wavefunction width. We apply the model to different types of nonlinear responses, eventually comparing the results with numerical simulations. Our model has the advantage of explaining the main properties of nonlinear confined waves, such as stability and breathing, in a relatively simple and intuitive manner.