Gas-dynamic approach to the theory of non-linear ion-acoustic waves in plasma with Kaniadakis’ distributed species

The non-linear theory of ion-acoustic waves in two-spesies isotropic collisionless plasma is developed. Both light electron and heavy ion species in the plasma are distributed with Kaniadakis’ statistics. Kaniadakis’ gas law is derived. The exact formula for the Sagdeev pseudopotential in parametric form is derived by the method based on the integration of the inverse function. The pseudopotential is analyzed. It is shown that periodic ion-acoustic waves and solitons are possible in the studied plasma. The differential equation describing the profile of the ion concentration in the wave is derived. The profiles of this concentration in the periodic ion-acoustic wave and soliton are calculated.