Accelerating self-modulated nonlinear waves in weakly and strongly magnetized relativistic plasmas

TL;DR

This paper demonstrates that a modified nonlinear Schrödinger equation in relativistic plasmas can be transformed into a second Painlevé equation, revealing accelerated wave solutions that differ from traditional solitons and depend on plasma magnetization.

Contribution

It introduces a novel connection between plasma wave equations and Painlevé equations, enabling the description of accelerated wave solutions in relativistic plasmas.

Findings

Wave solutions can accelerate and reverse direction.

Acceleration depends on plasma magnetization.

Solutions differ from standard solitons.

Abstract

It is known that a nonlinear Schr\"odinger equation describes the self-modulation of a large amplitude circularly polarized wave in relativistic electron-positron plasmas in the weakly and strongly magnetized limits. Here, we show that such equation can be written as a modified second Painlev\'e equation, producing accelerated propagating wave solutions for those nonlinear plasmas. This solution even allows the plasma wave to reverse its direction of propagation. The acceleration parameter depends on the plasma magnetization. This accelerating solution is different to the usual soliton solution propagating at constant speed.