Multi-dimensional instability of electrostatic solitary structures in magnetized nonthermal dusty plasmas

A rigorous theoretical investigation has been made of multi-dimensional instability of obliquely propagating electrostatic solitary structures in a hot, magnetized, non-thermal dusty plasma which consists of a negatively charged hot dust fluid, Boltzmann distributed electrons and nonthermally distributed ions. The Zakharov–Kuznetsov equation for the electrostatic solitary structures that exist in such a dusty plasma system is derived by the reductive perturbation method. The multi-dimensional instability of these solitary waves is also studied by the small-k (long wavelength plane wave) perturbation expansion method. The nature of these solitary structures, the instability criterion and their growth rate depending on dust-temperature, external magnetic field and obliqueness are discussed. The implications of these results to some space and astrophysical dusty plasma situations are briefly mentioned.