  Droplet solitons are a strongly nonlinear, inherently dynamic structure in
the magnetization of ferromagnets, balancing dispersion (exchange energy) with
focusing nonlinearity (strong perpendicular anisotropy). Large droplet solitons
have the approximate form of a circular domain wall sustained by precession
and, in contrast to single magnetic vortices, are predicted to propagate in an
extended, homogeneous magnetic medium. In this work, multiscale perturbation
theory is utilized to develop an analytical framework for investigating the
impact of additional physical effects on the behavior of a propagating droplet.
After first developing soliton perturbation theory in the general context of
Hamiltonian systems, a number of physical phenomena of current interest are
investigated. These include droplet-droplet and droplet-boundary interactions,
spatial magnetic field inhomogeneities, spin transfer torque induced forcing in
a nanocontact device, and damping. Their combined effects demonstrate the
fundamental mechanisms for a previously observed droplet drift instability and
under what conditions a slowly propagating droplet can be supported by the
nanocontact, important considerations for applications. This framework
emphasizes the particle-like dynamics of the droplet, providing analytically
tractable and practical predictions for modern experimental configurations.
