Blow-up solitons at the nonlinear stage of the two-stream instability in quantum plasmas

TL;DR

This paper investigates the nonlinear evolution of the quantum two-stream instability in plasmas, revealing blow-up solitons and unstable modes described by elliptic nonlinear equations, with solutions that diverge in finite time.

Contribution

It introduces a novel analysis of the nonlinear stage of quantum two-stream instability, identifying blow-up solitons and unstable modes in a plasma context.

Findings

Both nonlinear solutions blow up in finite time.

Identified two types of solutions: unstable mode and pulsating soliton.

Nonlinear stage described by elliptic nonlinear string equation.

Abstract

The nonlinear evolution of the quantum two-stream instability in a plasma with counter-streaming electron beams is studied. It is shown that in the long-wave limit the nonlinear stage of the instability can be described by the elliptic nonlinear string equation. We present two types of the nonlinear solutions. The first one is an unstable nonlinear mode that is continuously related with the growing linear solution and the second one is a pulsating soliton. We show that both of these solutions blow up in a finite time.