Abstract
The nonlinear three-dimensional modified Zakharov–Kuznetsov (mZK) equation governs the behavior of weakly nonlinear ion-acoustic waves in a plasma comprising cold ions and hot isothermal electrons in a presence of a uniform magnetic field. By using the reductive perturbation procedure leads to a mZK equation governing the propagation of ion dynamics of nonlinear ion-acoustic waves in a plasma. The mZK equation has solutions that represent solitary traveling waves. We found the electrostatic field potential and electric field in form traveling wave solutions for three-dimensional mZK equation. The solutions for the mZK equation are obtained precisely and efficiency of the method can be demonstrated. The stability of solitary traveling wave solutions of the mZK equation to three-dimensional long-wavelength perturbations are investigated.