Nonplanar dust-acoustic waves and chaotic motions in Thomas Fermi dusty plasmas

The properties of linear and nonlinear nonplanar dust acoustic (DA) solitary waves and chaotic behavior are investigated in an unmagnetized Thomas Fermi dusty plasma, whose components are degenerate electrons, ions, and negatively charged inertial cold dust grains. A linear dispersion relation is obtained and solved numerically. It has been observed that linear excitation characteristics are influenced by radial distance r, geometric term nu, and ion-to-electron Fermi temperature ratio sigma(i). We have also noted that the addition of a geometrical term in dispersion relation gives damping along the radial axis. A modified Korteweg-de Vries (KdV) equation is derived by employing the reductive perturbation technique, and its numerical solutions are obtained. The modified KdV equation is discussed for cold dust grains in planar and nonplanar frameworks. Upon the introduction of external periodic perturbation, the perturbed modified KdV equation is studied in planar geometry via some qualitative and quantitative approaches. The perturbed KdV equation can give rise to the periodic, quasiperiodic, and chaotic motions for DA waves. The strength of the external perturbation and dust concentration h play the major role of the switching parameter in the transition of dynamic motion. The developed chaos can be weakened with the variation of dust concentration h. It has been observed that the dust concentration affects the dynamics of DA waves in planar geometry which is an important observation in this study. Published by AIP Publishing.