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

2013/04/05 by M. Burak Erdoğan, M. Burak Erdogan, Jeremy L. Marzuola +6
Mathematics · Physics and Astronomy · #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP #msc:35Q55

paper · pdf · doi:10.48550/arxiv.1304.1596

16 pages, 7 figures

openalex publication_date 2013/04/05 · arxiv created 2015/02/06 · arxiv updated 2015/02/09 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

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.

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