“Extraordinary” modulation instability in optics and hydrodynamics

Abstract

The classical theory of modulation instability (MI) attributed to Bespalov–Talanov in optics and Benjamin–Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact weakly nonlinear theory of wave propagation. We report results of experiments in both optics and hydrodynamics, which are in excellent agreement with nonlinear theory. These observations clearly demonstrate that MI has a wider band of unstable frequencies than predicted by the linear stability analysis. The range of areas where the nonlinear theory of MI can be applied is actually much larger than considered here.

Localized nonlinear waves on spatio-temporally controllable backgrounds for a (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq model in water waves

“…Recently, the impact of nonlinear propagation of periodically varying background (dn-and cn-periodic waves) on the solitons and rogue waves has been observed experimentally in the NLS framework with arbitrarily shaped light waves in optical fibers and a common water wave tank [23][24][25]. So, it is of potential physical importance to understand such scenario in other nonlinear models too.…”

“…However, the possibility of such nonlinear wave occurrence on varying backgrounds with controllable features becomes an open question and it started to attract interest among the researchers due to the physical significance and realization in different contexts. Particularly, the physical motivation to look for such nonlinear waves on non-uniform/varying backgrounds starts from the situation of randomly varying surface or deep water waves to inhomogeneous plasma, layered magnetic materials, inhomogeneous optical media, and atomic condensate system [22][23][24][25]. As a result of this search, some localized nonlinear waves on varying backgrounds are investigated in recent times, which include the rogue waves on cnoidal, periodic, and solitary wave backgrounds in one-dimensional models such as focusing NLS model [26][27][28][29], derivative NLS equation [30][31][32], higher-order nonlinear Schrödinger equation [33,34], higher-order modified KdV equation [35], modified KdV models [36,37], Hirota equation [38,39], Gerdjikov-Ivanov model [40], sine-Gordon equation [41,42], Fokas model [43], and coupled cubic-quintic NLS equation [44] as well as vector Chen-Lee-Liu NLS model [45].…”

Manipulation of breather waves with split-dispersion cascaded fibers

“…A typical example is given by a compressed 'pulse trains' formed by coherent seed-induced modulation instability (MI), i.e., breather solutions of the integrable nonlinear Schrödinger equation (NLSE) for which their dynamics describe the growth-decay evolution of MI [1][2][3][4][5][6]. Furthermore, coherent seed-induced breathers in various conservative setting inevitably manifest as a synchronized periodic oscillation along longitudinal evolution [7][8][9][10]. Consequently, all possibilities to 'stabilize' a breather wave and especially to freeze breather's amplitude and phase in a controllable manner are of great interest [11][12][13][14].…”

Modulation instability and non-degenerate Akhmediev breathers of Manakov equations

“…MI is closely connected to emergence of rogue waves [8][9][10][11]. It is directly related to recurrence phenomena [12][13][14][15][16][17][18]. MI leads to breather formation [19][20][21][22][23][24].…”