  Propagating, solitary magnetic wave solutions of the Landau-Lifshitz equation
with uniaxial, easy-axis anisotropy in thin (two-dimensional) magnetic films
are investigated. These localized, nontopological wave structures, parametrized
by their precessional frequency and propagation speed, extend the stationary,
coherently precessing "magnon droplet" to the moving frame, a non-trivial
generalization due to the lack of Galilean invariance. Propagating droplets
move on a spin wave background with a nonlinear droplet dispersion relation
that yields a limited range of allowable droplet speeds and frequencies. An
iterative numerical technique is used to compute the propagating droplet's
structure and properties. The results agree with previous asymptotic
calculations in the weakly nonlinear regime. Furthermore, an analytical
criterion for the droplet's orbital stability is confirmed. Time-dependent
numerical simulations further verify the propagating droplet's robustness to
perturbation when its frequency and speed lie within the allowable range.
