Регистрация / Вход
Прислать материал

Collisions of coherent structures and formation of rogue waves in NLSE

Name
Andrey
Surname
Gelash
Scientific organization
Novosibirsk State University
Academic degree
Ph.D.
Position
researcher
Scientific discipline
Physics & Astronomy
Topic
Collisions of coherent structures and formation of rogue waves in NLSE
Abstract
In this work we present numerical simulation of modulation instability of the condensate and cnoildal wave. For this experiments we discuss probability of rogue waves formation from randomly perturbed initial conditions in terms of breathers collisions. We propose different statistical models of solitonic and breathers gas. One of this models is based on our recent work devoted to the theoretical and experimental study of the so called super-regular NLSE breathers which play a special role in the NLSE dynamics.
Keywords
solitons, nonlinear waves
Summary

Collisions of coherent structures and formation of rogue waves in NLSE

A.A. Gelash1, D.S. Agafontsev1,2, E.A. Kuznetsov1,3,4 and V.E. Zakharov1,3,4

1. Novosibirsk State University, Novosibirsk, 630090, Russia

2. P.P. Shirshov Institute of Oceanology, Moscow 117218, Russia.

3. Lebedev Physical Institute, Russian Academy of Sciences, Moscow, 119991, Russia

4. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Chernogolovka, Moscow region, 142432, Russia

Collisions of coherent structures such as solitons or breathers is the main mechanism of rogue waves formation in the nonlinear Schrodinger equation (NLSE) and other integrable systems. The statistical description of this process is the question of great importance for the practical applications and for the theory of integrable turbulence [1]. The full integrability of NLSE gives enormous advantages for the construction of the theory for rogue waves formation. Using the inverse scattering transform one can analyse wave field in terms of spectrum for the Zakharov-Shabat system. It allows to distinguish coherent structures and to predict properties of their collitions.


In this work we present numerical simulation of modulation instability of the condensate and cnoildal wave [1,2]. For this experiments we discuss probability of rogue waves formation from randomly perturbed initial conditions in terms of breathers collisions. We propose different statistical models of solitonic and breathers gas. One of this models is based on our recent work devoted to the theoretical and experimental study of the so called super-regular NLSE breathers [3,4] which play a special role in the NLSE dynamics.

[1] Agafontsev, D. S., and Vladimir E. Zakharov. "Integrable turbulence and formation of rogue waves." Nonlinearity 28.8 (2015): 2791.
[2] Agafontsev, D. S., and V. E. Zakharov. "Integrable turbulence generated from modulation instability of cnoidal waves." arXiv preprint arXiv:1512.06332 (2015). Under review.
[3] Gelash, A. A., and Vladimir E. Zakharov. "Superregular solitonic solutions: a novel scenario for the nonlinear stage of modulation instability." Nonlinearity 27.4 (2014): R1.
[4] Kibler, B., Chabchoub, A., Gelash, A., Akhmediev, N., and Zakharov, V. E."Superregular breathers in optics and hydrodynamics: Omnipresent modulation instability beyond simple periodicity." Physical Review X 5.4 (2015): 041026.