  Considering the non-hydrostatic mass flow model (Pudasaini, 2022), here, we
derive a novel dispersive wave equation for landslide. The new dispersive wave
for landslide recovers the classical dispersive water waves as a special case.
We show that the frequency dispersion relation for landslide is inherently
different than the classical frequency dispersion for water waves. The wave
frequency with dispersion increases non-linearly as a function of the wave
number. For dispersive landslide, the wave frequency without dispersion appears
to heavily overestimate the dispersive wave frequency for higher wave number.
Due to the dispersion term emerging from the non-hydrostatic contribution for
landslide, the phase velocity becomes a function of the wave number. This gives
rise to the group velocity that is significantly different from the phase
velocity, characterizing the dispersive mass flow. The dispersive phase
velocity and group velocity decrease non-linearly with the wave number. Yet,
the group velocity is substantially lower than the phase velocity. We
analytically derive a dispersion number as the ratio between the phase velocity
and the group velocity, which measures the deviation of the group velocity from
the phase velocity, provides a dynamic scaling between them and summarizes the
overall effect of dispersion in the mass flow. The dispersion number for
landslide increases rapidly with the wave number, which is in contrast to the
dispersion in water waves. With the definition of the effective dispersive
lateral stress, we prove the existence of an anti-restoring force in landslide.
We reveal the fact that due to the anti-restoring force, landslides are more
dispersive than the piano strings. So, the wave dispersion in landslide is
fundamentally different than the wave dispersion in the piano string. Our model
constitutes a foundation for the wave phenomenon in dispersive mass flows.
