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.
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