This thesis presents the nonlinear propagation dynamics in isotropic media. The influence of initial conditions on the propagation dynamics is considered. Three different instances are considered. We experimentally and numerically study the influence the temporal profile of a laser pulse has on the propagation and collapse dynamics when propagating in different group velocity dispersion regimes. We are interested in the spatio-temporal collapse dynamics of super-Gaussian pulses in this regime. We find that with a super-Gaussian pulse, we see pulsesplitting in this regime. We numerically study how the transverse beam profile effects the propagation in waveguide structures, both step-index fibers and hollow metallic waveguides. We are interested in modes that are necklace beams, with the possibility of application for highpower fiber lasers and amplifiers. We find that there is a benefit in the power threshold for collapse, but that is depends strongly on exciting the desired mode. Finally, we experimentally study the propagation of high power beams, which interact due to the Kerr nonlinearity. The main interest is in the propagation under conditions in which they exhibit spiral motion. We see large rotation of about 40 degrees when the collapsing beams are interacting.