  We demonstrate that laser beam collapse in highly nonlinear media can be
described, for a large number of experimental conditions, by the geometrical
optics approximation within high accuracy. Taking into account this fact we
succeed in constructing analytical solutions of the eikonal equation, which are
exact on the beam axis and provide: i) a first-principles determination of the
self-focusing position, thus replacing the widely used empirical Marburger
formula, ii) a benchmark solution for numerical simulations, and iii) a tool
for the experimental determination of the high-order nonlinear susceptibility.
Successful comparison with several experiments is presented.
