  The unsteady, nonlinear magnetization dynamics induced by spin injection in
an easy-plane ferromagnetic channel subject to an external magnetic field are
studied analytically. Leveraging a dispersive hydrodynamic description, the
Landau-Lifshitz equation is recast in terms of hydrodynamic-like variables for
the magnetization's perpendicular component (spin density) and azimuthal phase
gradient (fluid velocity). Spin injection acts as a moving piston that
generates nonlinear, dynamical spin textures in the ferromagnetic channel with
downstream quiescent spin density set by the external field. In contrast to the
classical problem of a piston accelerating a compressible gas, here, variable
spin injection and field lead to a rich variety of nonlinear wave phenomena
from oscillatory spin shocks to solitons and rarefaction waves. A full
classification of solutions is provided using nonlinear wave modulation theory
by identifying two key aspects of the fluid-like dynamics: subsonic/supersonic
conditions and convex/nonconvex hydrodynamic flux. Familiar waveforms from the
classical piston problem such as rarefaction (expansion) waves and shocks
manifest in their spin-based counterparts as smooth and highly oscillatory
transitions, respectively. The spin shock is an example of a dispersive shock
wave, which arises in many physical systems. New features without a gas
dynamics counterpart include composite wave complexes with "contact" spin
shocks and rarefactions. Magnetic supersonic conditions lead to two pronounced
piston edge behaviors including a stationary soliton and an oscillatory
wavetrain. These coherent wave structures have physical implications for the
generation of high frequency spin waves from pulsed injection and persistent,
stable stationary and/or propagating solitons in the presence of magnetic
damping. The analytical results are favorably compared with numerical
simulations.
