The dispersion and landau damping of the dispersive Alfvén waves (DAW) have been studied in the plasma with nonextensive electrons and ions. The conditions for the existence of inertial Alfvén waves (IAW) and kinetic Alfvén waves (KAW) are modified by electrons' nonextensive parameter qe. For IAW, βq ≪ me/mi; for KAW, me/mi ≪ βq ≪ 1, βq is the ratio of the effective thermal pressure to the magnetic pressure. In the plasma with superthermal particles, the frequency of the IAW and KAW will increase with the increase of qe when the effective temperature of the plasma systems keeps invariant. Whereas the damping rates of the IAW and KAW vary inversely with respect to qe for the reason that the phase velocity of KAW is much smaller than the effective thermal velocity, while the phase velocity of IAW is much bigger than the effective thermal velocity.
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