Abstract
The problem of nonlinear ion-acoustic waves equation in a magnetized plasma, known as Zakharov-Kuznetsov equation, is investigated by using symmetry analysis. The carryover of the symmetry analysis has led to certain similarity reductions of this equation. Furthermore, exact solutions of similarity reductions are obtained by modified Exp-Function method with computational symbolic. Some figures are obtained to show the properties of the solutions.
Highlights
There are many well-known methods to obtain exact solutions [1 − 5]
The carryover of the symmetry analysis has led to certain similarity reductions of this equation
Exact solutions of similarity reductions are obtained by modified Exp-Function method with computational symbolic
Summary
There are many well-known methods to obtain exact solutions [1 − 5]. In order to unite and widen various specialized solution method for partial differential equations Lie introduced the notion of continuous groups know as Lie groups. contiuing his investigations he shown that partial differential equation can be reduced to many ordinary differential equations which is led to varied solutions. In order to unite and widen various specialized solution method for partial differential equations Lie introduced the notion of continuous groups know as Lie groups. Consider the nonlinear ion-acoustic waves equation which is called (1+3)-dimensional Zakharov-Kuznetsov (Zk) equation [10, 11] in the following form: ut + p1u ux + p2ux,x,x + p3ux,y,y + p4ux,z,z = 0. ZK [10] is described the diffusion of nonlinear ion-acoustic waves in magnetized plasma [10] This equation was devoted to study many properties including presence and stability of solitary wave solutions for the ZK model [10, 13 − 15]. From the commutator relations in table 1, we utilized the following six non-equivalent possibilities of Lie algebra (I)V1 + m1V2 + m2V4 + m3V5 + m4V6 + m5V7, (II)V2 + m1V4 + m2V5 + m3V6 (III)V4 + m1V5 + m2V7 (IV)V2 + m1V5 + m2V7 (V)V2 + m1V4 + m2V7 (VI)V2 + m1V4 + m2V5
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