Dust ion acoustic solitary waves and their multi-dimensional instability in a weakly relativistic adiabatic magnetized dusty plasma with two different types of adiabatic electrons

Obliquely propagating dust ion-acoustic solitary waves in a collisionless, weakly relativistic, adiabatic, magnetized dusty plasma which consist of two different types of adiabatic inertia-less electrons, weakly relativistic adiabatic inertial ions fluid and negatively charged stationary dust particles have been studied. A nonlinear Zakharov–Kuznetsov equation has been derived by using reductive perturbation method. Solitary wave solution of this equation has been obtained. Combined effects of the external magnetic field, obliqueness, relativistic factor and two-temperature adiabatic electrons, which are found to significantly modify the basic properties of dust ion acoustic solitary waves, are explicitly examined. Multi-dimensional instability of dust ion acoustic solitary waves has been analyzed using small-k perturbation expansion technique. The results show that the external magnetic field, propagation angle, relativistic factor and temperature ratio between low and high temperatures adiabatic electrons have strong effects on instability criterion as well as growth rate of instability.