The European Physical Journal Special Topics

, Volume 147, Issue 1, pp 25–43

The modulation instability revisited

  • H. Segur
  • D. M. Henderson
Article

DOI: 10.1140/epjst/e2007-00201-1

Cite this article as:
Segur, H. & Henderson, D. Eur. Phys. J. Spec. Top. (2007) 147: 25. doi:10.1140/epjst/e2007-00201-1

Abstract.

The modulational instability (or “Benjamin-Feir instability”) has been a fundamental principle of nonlinear wave propagation in systems without dissipation ever since it was discovered in the 1960s. It is often identified as a mechanism by which energy spreads from one dominant Fourier mode to neighboring modes. In recent work, we have explored how damping affects this instability, both mathematically and experimentally. Mathematically, the modulational instability changes fundamentally in the presence of damping: for waves of small or moderate amplitude, damping (of the right kind) stabilizes the instability. Experimentally, we observe wavetrains of small or moderate amplitude that are stable within the lengths of our wavetanks, and we find that the damped theory predicts the evolution of these wavetrains much more accurately than earlier theories. For waves of larger amplitude, neither the standard (undamped) theory nor the damped theory is accurate, because frequency downshifting affects the evolution in ways that are still poorly understood.

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  • H. Segur
    • 1
  • D. M. Henderson
    • 2
  1. 1.Department of Applied MathematicsUniversity of ColoradoBoulderUSA
  2. 2.Department of Mathematics, Penn State UniversityW.G. Pritchard Fluid Mechanics LaboratoryUniversity ParkUSA