Short-wavelength soliton in a fully degenerate quantum plasma

TL;DR

This paper introduces a new nonlinear evolution equation for short-wavelength waves in a degenerate quantum plasma, revealing unique dispersion properties and elastic soliton collisions, expanding understanding of plasma wave dynamics.

Contribution

It develops a novel one-dimensional nonlinear equation for short-wavelength waves in degenerate quantum plasma, with unique dispersion and soliton collision properties.

Findings

Derived a new nonlinear evolution equation for quantum plasma waves.

Found soliton solutions with elastic collisions and phase shifts.

Revealed a distinct zero-sound dispersion relation.

Abstract

We present a novel one-dimensional nonlinear evolution equation governing the dynamics short-wavelength longitudinal waves in a nonrelativistic fully degenerate quantum plasma using kinetic equation for the Wigner function. The linear dispersion of the equation has a form of "zero sound" $\sim k\exp (-k^{2})$, where $k$ is the wave number, and it strongly differs from previously known nonlinear evolution equations. We numerically find the corresponding soliton solutions and demonstrate that the collisions between three solitons turn out to be elastic resulting only in phase shifts.