  Unsteady nonlinear magnetization dynamics are studied in an easy-plane
ferromagnetic channel subject to spin injection at one edge. The model
Landau-Lifshitz equation is known to support steady-state solutions, termed
dissipative exchange flows (DEFs) or spin superfluids. In this work, by means
of numerical simulations and theoretical analysis, we provide a full
description of the injection-induced, large-amplitude, nonlinear magnetization
dynamics up to the steady state. The dynamics prior to reaching steady state
are driven by spin injection, the perpendicular applied magnetic field, the
exchange interaction, and local demagnetizing fields. We show that the dynamics
take well-defined profiles in the form of rarefaction waves (RW), dispersive
shock waves (DSW), and solitons. The combination of these building blocks
depends on the interplay between the spin injection strength and the applied
magnetic field. A solitonic feature at the injection boundary, signaling the
onset of the magnetic "supersonic" condition at the injection edge, rapidly
develops and persists in the steady-state configuration of a contact soliton
DEF. We also demonstrate the existence of sustained soliton-train dynamics in
long time that can only arise in a nonzero applied magnetic field scenario. The
dynamical evolution of spin-injection-induced magnetization dynamics presented
here may help guide observations in long-distance spin transport experiments.
