@conference{
author = "Mančić, Ana and Maluckov, Aleksandra and Baronio, F. and Hadžievski, Ljupčo and Wabnitz, S.",
year = "2017",
abstract = "The emergence, dynamics and prediction of rogue waves (RW) have been in the focus of interest in diverse fields of science (oceanography, physics of fluids, optics, ultra cold matter, sociology, bio-sciemces) in the last decade [1]. Recently, we have started a study aimed to go deeply into the genesis and dynamics of multiparametric vector RW solutions in the context of the Manakov model by adopting statistical methods [2]. Particularity of vector RWs (semirational localized modes) is that they can feature both exponential and rational dependence on coordinates. These solutions can be reduced to the vector Peregrine solitons and bright- and dark-rogue wave composites for special parameter values [3,4]. Here, we present recent results of the preparatory phase of our study in which we try to find proper RW classifiers, like the significant wave height is in the context of scalar moedls in oceanography and optics [1]. Therefore, we firstly considered the 2D – vector generalization of the significant height vector as a classifier. It is defined as a vector quantity whose two components are related to the maximum absoulte deviation of the maplitude of corresponding RW components from the initial finite background field level. We consider as extreme ones those events characterized by the significant height vector whose components, either one or both, are above the threshold value. Particular, on-going effort is made in determing proper threshold values. The general vector form of the nonlinear Schrödinger equation, which can be written as: 𝑖 𝜕𝑢 (1) (𝑥,𝑡) 𝜕𝑡 + 𝜕 2𝑢 (1) (𝑥,𝑡) 𝜕𝑥 2 − (𝛾11|𝑢 (1) (𝑥,𝑡)| 2 +𝛾12|𝑢 (2) (𝑥,𝑡)| 2 ) 𝑢 (1) (𝑥,𝑡) = 0𝑖 𝜕𝑢 (2) (𝑥,𝑡) 𝜕𝑡 + 𝜕 2𝑢 (2) (𝑥,𝑡) 𝜕𝑥 2 − (𝛾21|𝑢 (1) (𝑥,𝑡)| 2 + 𝛾22|𝑢 (2) (𝑥,𝑡)| 2 ) 𝑢 (2) (𝑥,𝑡) = 0 and it was analyzed numerically by adopting the pseudo-spectral methods. The u (1)(x, t) and u (2)(x, t) represent the wave envelopes, γij (i, j=1,2) are inter (i ≠ j) and intra (i = j) nonlinear terms, t is the evolution variable, and x is a second independent variable. These equations reduces to Manakov system in the limit γij=g, i, j=1,2. The meaning of variables depends on the context (fluid dynamics, plasma physics, nonlinear optics, etc). It has been shown analytically and numericallythat different type of RWs can be observed in the presented model, depending on the system parameters [5]. This enables us to directly check our results with respect to various types of RWs. Statistical measures based on the height and amplitude distributions, their moments, return time statistics, etc, are numerically calculated. The study presented here is only a small fragment of our attempt to establish a full statistical analysis of the vector RWs.",
publisher = "Belgrade : Institute of Physics Belgrade",
journal = "PHOTONICA2017 : 6th International School and Conference on Photonics and COST actions: MP1406 and MP1402 : Program and the book of abstracts",
title = "Towards the fully developed statistical approach of vector rogue waves",
pages = "63-63",
url = "https://hdl.handle.net/21.15107/rcub_vinar_13350"
}