Plasma solitons in gated two-dimensional electron systems: exactly solvable analytical model for the regime beyond weak non-linearity

TL;DR

This paper presents an exact analytical model for plasma solitons in a 2D electron system near metallic gates, extending understanding beyond the weak non-linearity regime and providing detailed soliton characteristics.

Contribution

It introduces a non-perturbative, exactly solvable model for plasma solitons in 2D electron systems beyond weak non-linearity, which was not previously available.

Findings

Exact analytical description of soliton shape

Conditions for soliton existence derived

Relationship between amplitude, width, and velocity established

Abstract

We analytically study plasma solitary waves, or solitons, in a two-dimensional (2D) electron system (ES) placed in close proximity to and between two ideal metallic gates. As a rule, solitons are described using a perturbative approach applicable only in the weak non-linearity regime. In contrast, we analyze solitons considering a non-perturbative model. This framework enables an exact analytical description of the soliton shape. Moreover, it can be achieved in the regime beyond weak non-linearity -- when the concentration deviation due to the soliton is of the order of the equilibrium concentration. We determine the conditions required for a soliton to exist and derive the relationship between its amplitude, width, and velocity. We believe that our results obtained for the given model can provide valuable insight into the physics of non-linear waves.