  In the previous works harmonic, phase-mixed, Alfven wave dynamics was
considered both in the kinetic and magnetohydrodynamic regimes. Up today only
magnetohydrodynamic, phase-mixed, Gaussian Alfven pulses were investigated. In
the present work we extend this into kinetic regime. Here phase-mixed, Gaussian
Alfven pulses are studied, which are more appropriate for solar flares, than
harmonic waves, as the flares are impulsive in nature. Collisionless,
phase-mixed, dispersive, Gaussian Alfven pulse in transversely inhomogeneous
plasma is investigated by particle-in-cell (PIC) simulations and by an
analytical model. The pulse is in inertial regime with plasma beta less than
electron-to-ion mass ratio and has a spatial width of 12 ion inertial length.
The linear analytical model predicts that the pulse amplitude decrease is
described by the linear Korteweg de Vries (KdV) equation. The numerical and
analytical solution of the linear KdV equation produces the pulse amplitude
decrease in time as $t^{-1}$. The latter scaling law is corroborated by full
PIC simulations. It is shown that the pulse amplitude decrease is due to
dispersive effects, while electron acceleration is due to Landau damping of the
phase-mixed waves. The established amplitude decrease in time as $t^{-1}$ is
different from the MHD scaling of $t^{-3/2}$. This can be attributed to the
dispersive effects resulting in the different scaling compared to MHD, where
the resistive effects cause the damping, in turn, enhanced by the
inhomogeneity. Reducing background plasma temperature and increase in ion mass
yields more efficient particle acceleration.
