Modified Korteweg-de Vries solitons at supercritical densities in two-electron temperature plasmas

TL;DR

This paper investigates modified Korteweg-de Vries solitons in supercritical density plasmas with two-temperature electrons, revealing their properties, limitations in integrability, and comparison with Sagdeev solutions.

Contribution

It introduces a modified KdV equation with quartic nonlinearity for supercritical plasmas and compares its soliton solutions with full Sagdeev pseudopotential results.

Findings

mKdV solitons have larger amplitudes and widths than Sagdeev solutions

only slightly superacoustic mKdV solitons are physically acceptable

the mKdV equation with quartic nonlinearity is not fully integrable

Abstract

The supercritical composition of a plasma model with cold positive ions in the presence of a two-temperature electron population is investigated, initially by a reductive perturbation approach, under the combined requirements that there be neither quadratic nor cubic nonlinearities in the evolution equation. This leads to a unique choice for the set of compositional parameters and a modified Korteweg-de Vries equation (mKdV) with a quartic nonlinear term. The conclusions about its one-soliton solution and integrability will also be valid for more complicated plasma compositions. Only three polynomial conservation laws can be obtained. The mKdV equation with quartic nonlinearity is not completely integrable, thus precluding the existence of multi-soliton solutions. Next, the full Sagdeev pseudopotential method has been applied and this allows for a detailed comparison with the reductive perturbation results. This comparison shows that the mKdV solitons have slightly larger amplitudes and widths than those obtained from the more complete Sagdeev solution and that only slightly superacoustic mKdV solitons have acceptable amplitudes and widths, in the light of the full solutions.