Soliton solutions for a (3 + 1)-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov equation in a plasma

Abstract

Under investigation in this paper is a (3 + 1)-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation, which describes the nonlinear behaviors of ion-acoustic waves in a magnetized plasma where the cooler ions are treated as a fluid with adiabatic pressure and the hot isothermal electrons are described by a Boltzmann distribution. With the Hirota method and symbolic computation, we obtain the one-, two- and three-soliton solutions for such an equation. We graphically study the solitons related with the coefficient of the cubic nonlinearity [Formula: see text]. Amplitude of the one soliton increases with increasing [Formula: see text], but the width of one soliton keeps unchanged as [Formula: see text] increases. The two solitons and three solitons are parallel, and the amplitudes of the solitons increase with increasing [Formula: see text], but the widths of the solitons are unchanged. It is shown that the interactions between the two solitons and among the three solitons are elastic.