The Structure of Global Attractors for Dissipative Zakharov Systems with Forcing on the Torus

TL;DR

This paper investigates the dynamics of the dissipative Zakharov system on a torus, revealing stable periodic orbits and bifurcations as dissipation varies, through both numerical and analytical methods.

Contribution

It provides new insights into the structure of global attractors for the dissipative Zakharov system, combining numerical and analytical approaches.

Findings

Identification of stable periodic orbits and fixed points

Analysis of bifurcations with decreasing dissipation

Characterization of global attractor structure

Abstract

The Zakharov system was originally proposed to study the propagation of Langmuir waves in an ionized plasma. In this paper, motivated by earlier work of the first and third authors, we numerically and analytically investigate the dynamics of the dissipative Zakharov system on the torus in 1 dimension. We find an interesting family of stable periodic orbits and fixed points, and explore bifurcations of those points as we take weaker and weaker dissipation.