  The dynamics of nonlinear ion-acoustic solitary waves in the presence of
kinetic (Landau type) damping have been investigated in a collisionless,
non-magnetized electron-ion plasma. A cold ion fluid model, coupled to a
Vlasov-type kinetic equation for the electron dynamics, has been adopted as a
starting point. The electron population was assumed to be in a
kappa-distributed state, in account of the non-Maxwellian behavior of energetic
(suprathermal) electrons often observed in Space. A multiscale perturbation
technique has led to an evolution equation for the electrostatic potential, in
the form of a modified Korteweg-de Vries (KdV) equation, incorporating a
non-local term accounting for Landau damping (associated with the electron
statistics). Exact analytical solutions have been obtained, representing
solitary waves undergoing amplitude decay over time. The combined effect of
Landau damping and non-Maxwellian electron statistics (via the kappa parameter)
on the characteristics of IASWs has been examined. Numerical integration of the
evolution equation has been undertaken, to elucidate the importance of kinetic
Landau damping on a shock-shaped initial condition. The results of this
investigation aim to improve our understanding of the dynamics of nonlinear
electrostatic waves under the influence of Landau damping in various space
plasma environments.
