Effect of anisotropic dust pressure and κ-deformed Kaniadakis electrons on the propagation and stability of nonlinear dust acoustic waves

The propagation and stability of dust acoustic waves (DAWs) are studied based on a set of hydrodynamic equations of a collisionless, magnetized, and anisotropic dusty plasma. The plasma model consists of arbitrarily charged dust particles, along with Boltzmann-distributed ions and κ-deformed Kaniadakis electrons. The Chew–Goldberger–Low theory is also incorporated to characterize the anisotropic dust pressure. The Kaniadakis index κ does not contribute to nonlinear characteristics of the DAWs derived from the Zakharov–Kuznetsov (ZK) equation. Therefore, a modified ZK equation is derived, which can only be formulated in the case of positively charged dust grains. Furthermore, the small-wave number (small-k) expansion method is applied to analyze the stability of the steady-state solution of obliquely propagating DAWs. A key outcome is that the fundamental characteristics of the nonlinear wave are directly affected by the nature of the electron distribution (i.e., the Kaniadakis index), whereas the wave's stability remains unaffected by it at the lowest order of k. However, it is influenced by the magnetic field strength, pressure anisotropy, and other parameters.