Nail Akhmediev

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The conventional definition of rogue waves in the ocean is that their heights, from crest to trough, are more than about twice the significant wave height, which is the average wave height of the largest one-third of nearby waves. When modeling deep water waves using the nonlinear Schrödinger equation, the most likely candidate satisfying this criterion is(More)
Parametric curves featuring Hamiltonian versus energy are useful in the theory of solitons in conservative nonintegrable systems with local nonlinearities. These curves can be constructed in various ways. We show here that it is possible to find the Hamiltonian (H) and energy (Q) for solitons of non-Kerr-law media with local nonlinearities without specific(More)
Numerical simulations of the onset phase of continuous wave supercontinuum generation from modulation instability show that the structure of the field as it develops can be interpreted in terms of the properties of Akhmediev Breathers. Numerical and analytical results are compared with experimental measurements of spectral broadening in photonic crystal(More)
We present a method for finding the hierarchy of rational solutions of the self-focusing nonlinear Schrödinger equation and present explicit forms for these solutions from first to fourth order. We also explain their relation to the highest amplitude part of a field that starts with a plane wave perturbed by random small amplitude radiation waves. Our work(More)
The Akhmediev breather formalism of modulation instability is extended to describe the spectral dynamics of induced multiple sideband generation from a modulated continuous wave field. Exact theoretical results describing the frequency domain evolution are compared with experiments performed using single mode fiber around 1550 nm. The spectral theory is(More)
S. T. Cundiff,1 B. C. Collings,2,3 N. N. Akhmediev,4 J. M. Soto-Crespo,5 K. Bergman,2 and W. H. Knox3 1JILA, University of Colorado and National Institute of Standards and Technology, Boulder, Colorado 80309-0440 2Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544 3Bell Labs, Lucent Technologies, Holmdel, New Jersey(More)
With the use of a variant of the method of separation of variables, the initial value problem for the time-dependent linear Schrödinger equation is solved exactly for a large class of potential functions related to multisoliton interactions in the vector nonlinear Schrödinger equation. Completeness of states is proved for absolutely continuous initial data(More)
Nonlinear dissipative systems display the full (3+1)D spatiotemporal dynamics of stable optical solitons. We review recent results that were obtained within the complex cubic-quintic Ginzburg-Landau equation model. Numerical simulations reveal the existence of stationary bell-shaped (3+1)D solitons for both anomalous and normal chromatic dispersion regimes,(More)
Rare events of extremely high optical intensity are experimentally recorded at the output of a mode-locked fiber laser that operates in a strongly dissipative regime of chaotic multiple-pulse generation. The probability distribution of these intensity fluctuations, which highly depend on the cavity parameters, features a long-tailed distribution. Recorded(More)