Collision properties of overtaking supersolitons with small amplitudes

TL;DR

This paper investigates the collision behavior of small-amplitude supersolitons in plasma, deriving a modified Gardner equation and showing that collisions are inelastic, with supersolitons potentially transforming into regular solitons.

Contribution

It introduces a generalized KdV equation with quartic nonlinearity for supersolitons and analyzes their collision properties in plasma.

Findings

Supersoliton collisions are inelastic.

Supersolitons can transform into regular solitons after collisions.

Criteria for the existence of small-amplitude supersolitons are established.

Abstract

The collision properties of overtaking small-amplitude supersolitons are investigated for the fluid model of a plasma consisting of cold ions and two-temperature Boltzmann electrons. A reductive perturbation analysis is performed for compositional parameters near the supercritical composition. A generalized Korteweg-de Vries equation with a quartic nonlinearity is derived, referred to as the modified Gardner equation. Criteria for the existence of small-amplitude supersolitons are derived. The modified Gardner equation is shown to be not completely integrable, implying that supersoliton collisions are inelastic, as confirmed by numerical simulations. These simulations also show that supersolitons may reduce to regular solitons as a result of overtaking collisions.