Long-time dynamics of the modulational instability of deep water waves

M. J. Ablowitz, J. Hammack, Diane Marie Henderson, C. M. Schober

Research output: Contribution to journalArticlepeer-review

45 Scopus citations

Abstract

In this paper, we experimentally and theoretically examine the long-time evolution of modulated periodic 1D Stokes waves which are described, to leading-order, by the nonlinear Schrödinger (NLS) equation. The laboratory and numerical experiments indicate that under suitable conditions modulated periodic wave trains evolve chaotically. A Floquet spectral decomposition of the laboratory data at sampled times shows that the waveform exhibits bifurcations across standing wave states to left- and right-going modulated traveling waves. Numerical experiments using a higher-order nonlinear Schrödinger equation (HONLS) are consistent with the laboratory experiments and support the conjecture that for periodic boundary conditions the long-time evolution of modulated wave trains is chaotic. Further, the numerical experiments indicate that the macroscopic features of the evolution can be described by the HONLS equation. Ultimately, these laboratory experiments provide a physical realization of the chaotic behavior previously established analytically for perturbed NLS systems.

Original languageEnglish (US)
Pages (from-to)416-433
Number of pages18
JournalPhysica D: Nonlinear Phenomena
Volume152-153
DOIs
StatePublished - May 15 2001

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Long-time dynamics of the modulational instability of deep water waves'. Together they form a unique fingerprint.

Cite this