  A novel type of solitary wave is predicted to form in spin torque oscillators
when the free layer has a sufficiently large perpendicular anisotropy. In this
structure, which is a dissipative version of the conservative droplet soliton
originally studied in 1977 by Ivanov and Kosevich, spin torque counteracts the
damping that would otherwise destroy the mode. Asymptotic methods are used to
derive conditions on perpendicular anisotropy strength and applied current
under which a dissipative droplet can be nucleated and sustained. Numerical
methods are used to confirm the stability of the droplet against various
perturbations that are likely in experiments, including tilting of the applied
field, non-zero spin torque asymmetry, and non-trivial Oersted fields. Under
certain conditions, the droplet experiences a drift instability in which it
propagates away from the nanocontact and is then destroyed by damping.
