“…17,18 The transverse Gaussian field distribution, which is the fundamental mode in linear paraxial resonators, is widely used as an approximate description for the transverse field distribution in nonlinear resonators. 3,4,19 In addition, the Gaussian trial function can conveniently be characterized in terms of the complex q parameters, which allow for a compact description of the optical propagation based on the ABCD matrix formalism. 15,16 In the following, the Gaussian equations of motion, obtained by the Kantorovitch method, are given for the spatial beam propagation and the temporal pulse evolution in a Kerr medium with a parabolic transverse and spectral gain profile, as well as for the full spatiotemporal dynamics.…”