Nonlinear evolution and propagation of KdV solitons using fully kinetic PIC simulations

In this study, we conduct a comprehensive investigation into the behavior of ion acoustic solitary waves (solitons) of varying amplitude launched into a one-dimensional plasma in the laboratory frame utilizing fully kinetic particle-in-cell (PIC) simulations. The initial conditions for the ion density, velocity, and potential are prescribed according to the solution of the Korteweg-de Vries (KdV) equation, while the electron density is initialized based on the solution of Poisson's equation at the initial time step, treating ions as a cold species and assigning a temperature to the electrons. Our findings reveal that small amplitude solitons maintain their initial KdV state with negligible particle trapping, whereas larger amplitude solitons exhibit nonlinear evolution to a saturated state at a higher amplitude that deviates from the KdV soliton, with nonlinear effects arising from particle trapping. In particular, we find that the soliton amplitude oscillates roughly at the electron bounce frequency. The soliton ion density, potential, and velocity are found to exhibit better agreement with a modified KdV equation, which incorporates a nonlinear term to capture trapping phenomena or a nonlinear term due to higher order dispersive effects. Furthermore, our results demonstrate that the relationship between soliton speed and amplitude is inconsistent with existing theoretical predictions.