Collisionless damping of nonplanar dust acoustic waves due to dust charge fluctuation in nonextensive polarized plasma

A rigorous theoretical investigation has been made of the cylindrical/spherical dust acoustic waves in collisionless dusty plasma with variable charges under the influence of polarization force by reductive perturbation method. It is shown that the collisionless damping due to dust charge fluctuation causes the dust acoustic wave propagation to be described by the nonplanar damped Korteweg–de Vries equation. By use of weighted residual method, a progressive wave solution to nonplanar damped KdV equation is presented for the first time. It is shown that dust charge fluctuation produce damping which is responsible for wave attenuation. The solution shows that as one goes towards the axis of the cylinder or centre of the sphere, the wave attenuates faster and the effects are shown in some 2D figures. Within a small amplitude limit, the influence of dust charge fluctuation, polarisation power, nonextensivity and ion temperature on the time evolution of dust acoustic solitons is also demonstrated. In laboratory experiments and space regions, findings obtained here may shed light on the salient characteristics of DA waves. (paper)