High Relativistic Impact on Dust-Ion-Acoustic Solitary Waves in Unmagnetised Plasma with Kaniadakis Distributed Electrons

The dust-ion-acoustic solitary waves (DIASWs) traversing in an unmagnetised dusty plasma with cold ions and electrons that follow the \(\kappa\) $\kappa$ -deformed Kaniadakis distribution (KD) are described in this article. The Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations are generated by using the reductive perturbation method (RPM) to the basic equations. The implications of crucial parameters on the dynamics of solitary formations (namely, \(\kappa\) $\kappa$ -deformed parameter, dust concentration \(\mu\) $\mu$ , and relativistic factor \(\nu = \frac{{v_{0} }}{c}\) $\nu =\frac{v_0}{c}$ ) are studied in detail. It is important to report that compressive and rarefactive fast DIASWs are observed in the ranges \(\left( {\mu \le 0.66} \right)\) $\left(\mu \le 0.66\right)$ and \(\left( {\mu > 0.66} \right)\) $\left(\mu >0.66\right)$ respectively. Further, the parameter \(\kappa\) $\kappa$ has no effect on the DIASWs of the KdV equation. The current work may be useful in highlighting the salient features of high relativistic effects on DIASWs corresponding to the KdV and mKdV equations in laboratory plasmas, Earth’s magnetosphere in space plasmas, and pulsar magnetospheres of astrophysical plasmas.