  Stability of the well-known Walker propagating domain wall (DW) solution of
the Landau-Lifshitz-Gilbert equation is analytically investigated.
Surprisingly, the Walker's rigid body propagating DW mode is not stable against
the spin wave/wavepacket emission. In the low field region only stern spin
waves are emitted while both stern and bow waves are generated under high
fields. In a high enough field, but below the Walker breakdown field, the
Walker solution could be convective/absolute unstable if the transverse
magnetic anisotropy is larger than a critical value, corresponding to a
significant modification of the DW profile and DW propagating speed.
