TY - JOUR
T1 - The modulation instability revisited
AU - Segur, H.
AU - Henderson, D. M.
N1 - Funding Information:
We gratefully acknowledge financial support from the National Science Foundation NSF-DMS DMS-0139847. The experimental apparati were built with support from the Packard Foundation, the Sloan Foundation and the National Science Foundation, NSF-DMS 9972210.
PY - 2007/8
Y1 - 2007/8
N2 - 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 down shifting affects the evolution in ways that are still poorly understood.
AB - 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 down shifting affects the evolution in ways that are still poorly understood.
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U2 - 10.1140/epjst/e2007-00201-1
DO - 10.1140/epjst/e2007-00201-1
M3 - Article
AN - SCOPUS:34548363440
SN - 1951-6355
VL - 147
SP - 25
EP - 43
JO - European Physical Journal: Special Topics
JF - European Physical Journal: Special Topics
IS - 1
ER -