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We investigate dispersive and kinetic effects on the evolution of atwo-dimensional kinked Alfv\'en wave packet by comparing results from MHD,Hall-MHD and hybrid simulations of a low-$\beta$ plasma. We find that the Hallterm determines the overall evolution of the wave packet over a characteristictime $\tau^*=\tau_a\ell/d_i$ in both fluid and hybrid models. Dispersion of thewave packet leads to the conversion of the wave energy into internal plasmaenergy. When kinetic protons are considered, the proton internal energyincrease has contributions from both plasma compressions and phase spacemixing. The latter occurs in the direction parallel to the guiding meanmagnetic field, due to protons resonating at the Alfv\'en speed with acompressible mode forced by the wave packet. Implications of our results forswitchbacks observations and solar wind energetics are discussed.

Dispersive and kinetic effects on kinked Alfv\'en wave packets: a comparative study with fluid and hybrid models