Generation of dispersion in nondispersive nonlinear waves in thermal equilibrium

Wonjung Lee, Gregor Kovačič, David Cai

Research output: Contribution to journalArticlepeer-review


In this work, we examine the important theoretical question of whether dispersion relations can arise from purely nonlinear interactions among waves that possess no linear dispersive characteristics. Using two prototypical examples of nondispersivewaves,we demonstrate how nonlinear interactions can indeed give rise to effective dispersive-wave-like characteristics in thermal equilibrium. Physically, these example systems correspond to the strong nonlinear coupling limit in the theory of wave turbulence. We derive the form of the corresponding dispersion relation, which describes the effective dispersive structures, using the generalized Langevin equations obtained in the Zwanzig-Mori projection framework.Weconfirm the validity of this effective dispersion relation in our numerical study using the wavenumber-frequency spectral analysis. Our work may provide insight into an important connection between highly nonlinear turbulent wave systems, possibly with no discernible dispersive properties, and the dispersive nature of the corresponding renormalized waves.

Original languageEnglish (US)
Pages (from-to)3237-3241
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number9
StatePublished - Feb 26 2013


  • Dispersive waves
  • Fermi-Pasta-Ulam chain
  • Majda-McLaughlin-Tabak model
  • Nonlinear systems
  • Nonlinearity-induced resonances

ASJC Scopus subject areas

  • General


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