Stability of solitary kinetic Alfvén waves and ion-acoustic waves in a nonthermal plasma

The KdV-ZK (Korteweg–de Vries–Zakharov–Kuznetsov) equations for kinetic Alfvén and ion-acoustic waves in a nonthermal magnetized plasma have been derived. The coefficient of the nonlinear term of this equation for an ion-acoustic wave can vanish along a curve in a two-dimensional parameter space. In this case, two coupled equations constituting a modified KdV-ZK equation describing nonlinear behavior of an ion-acoustic wave are derived. The solitary wave solutions of all these equations are obtained and their stabilities are investigated by the Rowlands–Infeld method. It is found that the kinetic Alfvén solitons are stable. The instability conditions and the maximum growth rate of the instability for ion-acoustic solitons are determined.