Stability analysis solutions for nonlinear three-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in a magnetized electron-positron plasma

The nonlinear three-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov (mKdV-ZK) equation governs the behavior of weakly nonlinear ion-acoustic waves in magnetized electron-positron plasma which consists of equal hot and cool components of each species. By using the reductive perturbation procedure leads to a mKdV-ZK equation governing the oblique propagation of nonlinear electrostatic modes. The stability of solitary traveling wave solutions of the mKdV-ZK equation to three-dimensional long-wavelength perturbations is investigated. We found the electrostatic field potential and electric field in form traveling wave solutions for three-dimensional mKdV-ZK equation. The solutions for the mKdV-ZK equation are obtained precisely and efficiency of the method can be demonstrated. (C) 2016 Elsevier B.V. All rights reserved.