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Contributors
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- By Avishek Adhikari, Susanne E. Ahmari, Anne Marie Albano, Carlos Blanco, Desiree K. Caban, Jonathan S. Comer, Jeremy D. Coplan, Ana Alicia De La Cruz, Emily R. Doherty, Bruce Dohrenwend, Amit Etkin, Brian A. Fallon, Michael B. First, Abby J. Fyer, Angela Ghesquiere, Jay A. Gingrich, Robert A. Glick, Joshua A. Gordon, Ethan E. Gorenstein, Marco A. Grados, James P. Hambrick, James Hanks, Kelli Jane K. Harding, Richard G. Heimberg, Rene Hen, Devon E. Hinton, Myron A. Hofer, Matthew J. Kaplowitz, Sharaf S. Khan, Donald F. Klein, Karestan C. Koenen, E. David Leonardo, Roberto Lewis-Fernández, Jeffrey A. Lieberman, Michael R. Liebowitz, Sarah H. Lisanby, Antonio Mantovani, John C. Markowitz, Patrick J. McGrath, Caitlin McOmish, Jeffrey M. Miller, Jan Mohlman, Elizabeth Sagurton Mulhare, Philip R. Muskin, Navin Arun Natarajan, Yuval Neria, Nicole R. Nugent, Mayumi Okuda, Mark Olfson, Laszlo A. Papp, Sapana R. Patel, Anthony Pinto, Kristin Pontoski, Jesse W. Richardson-Jones, Carolyn I. Rodriguez, Steven P. Roose, Moira A. Rynn, Franklin Schneier, M. Katherine Shear, Ranjeeb Shrestha, Helen Blair Simpson, Smit S. Sinha, Natalia Skritskaya, Jami Socha, Eun Jung Suh, Gregory M. Sullivan, Anthony J. Tranguch, Hilary B. Vidair, Tor D. Wager, Myrna M Weissman, Noelia V. Weisstaub
- Edited by Helen Blair Simpson, Columbia University, New York, Yuval Neria, Columbia University, New York, Roberto Lewis-Fernández, Columbia University, New York, Franklin Schneier, Columbia University, New York
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- Book:
- Anxiety Disorders
- Published online:
- 10 November 2010
- Print publication:
- 26 August 2010, pp vii-xii
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- Chapter
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Stabilizing the Benjamin–Feir instability
- HARVEY SEGUR, DIANE HENDERSON, JOHN CARTER, JOE HAMMACK, CONG-MING LI, DANA PHEIFF, KATHERINE SOCHA
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- Journal:
- Journal of Fluid Mechanics / Volume 539 / 25 September 2005
- Published online by Cambridge University Press:
- 05 September 2005, pp. 229-271
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- Article
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The Benjamin–Feir instability is a modulational instability in which a uniform train of oscillatory waves of moderate amplitude loses energy to a small perturbation of other waves with nearly the same frequency and direction. The concept is well established in water waves, in plasmas and in optics. In each of these applications, the nonlinear Schrödinger equation is also well established as an approximate model based on the same assumptions as required for the derivation of the Benjamin–Feir theory: a narrow-banded spectrum of waves of moderate amplitude, propagating primarily in one direction in a dispersive medium with little or no dissipation. In this paper, we show that for waves with narrow bandwidth and moderate amplitude, any amount of dissipation (of a certain type) stabilizes the instability. We arrive at this stability result first by proving it rigorously for a damped version of the nonlinear Schrödinger equation, and then by confirming our theoretical predictions with laboratory experiments on waves of moderate amplitude in deep water. The Benjamin–Feir instability is often cited as the first step in a nonlinear process that spreads energy from an initially narrow bandwidth to a broader bandwidth. In this process, sidebands grow exponentially until nonlinear interactions eventually bound their growth. In the presence of damping, this process might still occur, but our work identifies another possibility: damping can stop the growth of perturbations before nonlinear interactions become important. In this case, if the perturbations are small enough initially, then they never grow large enough for nonlinear interactions to become important.