The nonlinear Schrödinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface |
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| Authors: | A Chabchoub B Kibler C Finot G Millot M Onorato JM Dudley AV Babanin |
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| Institution: | 1. Centre for Ocean Engineering Science and Technology, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia;2. Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS, Université de Bourgogne, 21078 Dijon, France;3. Dipartimento di Fisica, Università degli Studi di Torino, Torino 10125, Italy;4. Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Torino, Torino 10125, Italy;5. Institut FEMTO-ST, UMR 6174 CNRS- Université de Franche-Comté, 25030 Besançon, France |
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| Abstract: | The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. a nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains. |
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| Keywords: | Electromagnetic waves Water waves Nonlinear Schrö dinger equation Benjamin&ndash Feir index |
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