Dipole-exchange spin wave pulses in magnetic thin films have been numerically modeled with the nonlinear Schrodinger equation. Small input pulse amplitudes yield propagating wave packets which exhibit a linear response. As the amplitude of the input pulse is increased, the propagating spin-wave pulse exhibits soliton and then multisoliton structures. In the soliton regime, three principal characteristics are observed. First, in the zero damping limit, the soliton propagates without changing its shape. Second, the soliton exhibits an inherent velocity in addition to its linear group velocity. Third, the soliton exhibits a damping rate that is approximately twice that in the linear regime.