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

摘要

The Zakharov system was originally proposed to study the propagation of Langmuir waves in an ionized plasma. In this paper, motivated by the work of the first and third authors in [Anal. Partial Differential Equations, 6 (2013), pp. 723-750], we numerically and analytically investigate the dynamics of the dissipative Zakharov system on the torus in one 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.