Effects of dust size distribution on dust acoustic waves in magnetized two-ion-temperature dusty plasmas

A Zakharov–Kuznetsov (ZK) equation, a modified ZK (mZK) equation, and a coupled ZK (cZK) equation for small but finite amplitude dust acoustic waves in a magnetized two-ion-temperature dusty plasma with dust size distribution have been investigated in this paper. The variations of the linear dispersion relation and group velocity, nonlinear solitary wave amplitude, and width with an arbitrary dust size distribution function are studied numerically. We conclude that they all increase as the total number density of dust grains increases, and they are greater for unusual dusty plasma (the number density of larger dust grains is greater than that of smaller dust grains) than that of usual dusty plasma (the number density of smaller dust grains is greater than that of larger dust grains). It is noted that the frequency of the linear wave increases as the wave number along the magnetic direction increases. Furthermore, the width of the nonlinear waves increases but its amplitude decreases as the wave number along the magnetic direction increases.