Journal
JETP LETTERS
Volume 98, Issue 11, Pages 731-734Publisher
MAIK NAUKA/INTERPERIODICA/SPRINGER
DOI: 10.1134/S0021364013240028
Keywords
-
Categories
Funding
- Ministry of Education and Science of the Russian Federation [11.G34.31.0035]
- Presidium of the Russian Academy of Sciences (program Fundamental Problems of Nonlinear Dynamics in Mathematical and Physical Sciences)
- Council of the President of the Russian Federation for Support of Young Scientists and Leading Scientific Schools
- Russian Foundation for Basic Research [12-01-00943-a, 13-01-00261, 11-05-01114-a]
Ask authors/readers for more resources
We examine statistics of waves for the problem of modulation instability development in the framework of discrete integrable Ablowitz-Ladik (AL) system. Modulation instability depends on one free parameter h that has the meaning of the coupling between the nodes on the lattice. For strong coupling h a parts per thousand(a) 1, the probability density functions (PDFs) for waves amplitudes coincide with that for the continuous classical nonlinear Schrodinger equation; the PDFs for both systems are very close to Rayleigh ones. When the coupling is weak h similar to 1, there appear highly localized waves with very large amplitudes, that drastically change the PDFs to significantly non-Rayleigh ones, with so-called fat tails when the probability of a large wave occurrence is by several orders of magnitude higher than that predicted by the linear theory. Evolution of amplitudes for such rogue waves with time is similar to that of the Peregrine solution for the classical nonlinear Schrodinger equation.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available