Abstract
The nonlinear amplitude modulation of low-frequency electrostatic ion waves propagating in collisionless magnetized electron-positron-ion plasma are studied. The Krylov-Bogoliubov-Mitropolsky perturbation method is employed to derive the nonlinear Schrödinger equation. Modulation instability of both ion-acoustic and ion-cyclotronlike modes is examined. We found that the ion-acoustic mode, which propagates below the ion-cyclotron frequency, is stable if the strength of the external magnetic field is small. However, as the strength of the magnetic field increases, this mode becomes modulationally unstable for a range of wave numbers and angles of propagation. This range increases as the strength of the magnetic field and/or positron density increases. For the ion-cyclotronlike mode, which propagates above the ion-cyclotron frequency, a number of stability/instability regions appear in the
(
k
c
,
θ
)
plane even for a very small value of the magnetic field. It is found that, for both modes, critical wave number
k
c
separating the stability and instability regions, shifts towards higher values as the density of the positron increases.