Modification of Korteweg--de Vries solitons in plasmas by resonant particles

A perturbed Korteweg--de Vries equation describing the influence of resonant electrons on a Trivelpiece--Gould soliton is solved numerically, and the results are compared with predictions from the perturbation analysis of the equation by Karpman and Maslov. The range of parameters for which the perturbation approach is valid is determined, and it is shown that for parameters that are within the perturbation validity limits the modifying effects on the soliton are negligible. However, it is demonstrated that the theoretical results from the perturbation analysis are good approximations even in cases of strong soliton modification. Examples are given both of soliton damping and soliton amplification, and it is shown that the numerical solutions also can be interpreted as describing the modification of an ion-acoustic soliton by resonant particles