Small Amplitude Nonlinear Dust Ion Acoustic Waves in a Magnetized Dusty Plasma With Charge Fluctuation

A theoretical investigation of one dimensional dynamics of nonlinear electrostatic dust ion acoustic waves in a magnetized dusty plasma has been made by reductive perturbation technique. The effects of both the adiabatic and the nonadiabatic dust charge variation are incorporated. The most interesting feature is that the nonlinear evolution equation of the dust ion acoustic wave for nonadiabatic dust charge variation is the Korteweg-de Vries (KdV) Burger equation, whereas for adiabatic dust charge variation, the equation is the KdV equation. A nonadiabaticity generated anomalous dissipative effect causes generation of dust ion acoustic shock waves, a new mechanism for the generation of shock waves. Numerical integration of the KdV Burger equation shows that dust ion acoustic waves admit oscillatory (dispersion dominant) or monotone (dissipation dominant) shock solutions. It is also seen that the magnetic field and the dust charge variations significantly modify the wave amplitude.