Rogue Breathers Research Articles

Dynamics of recurrent modulational instability near its separatrix in nonlinear fiber optics

Separatrix crossing stands for the continuation of the modulation instability into the strong depleted regime and is responsible for the symmetry breaking nature of the recurrence phenomenon. The near-separatrix dynamic for recurrent modulational instability is of great importance because it is closely associated with the formation of rogue breather structures. Here, we have developed the underlying phase-space structure of nonlinear modulation instability by treating the three-mode truncate model as a simple oscillator. This allowed us to reveal the high sensitivity of the switching dynamics characterized by inner or outer trajectories to the initial condition around a separatrix. Our results present a major step forward towards the complete understanding of recurrent modulational instability in a truly conservative setting and can provide a guidance to experimentally measure the involved recursive behaviors.

Rogue breathers and rogue lumps on a background of dark line solitons for the Maccari system

The Maccari system is a nonlinear dynamical model for the description of two-dimensional rogue waves occuring in diverse physical settings. For this two-dimensional nonlinear system, the time localized breathers and doubly localized lumps termed as rogue breathers and rogue lumps on a background of dark line solitons are investigated. The rogue breather behaves as a breather appearing and disappearing on a background of two dark line solitons, and is generated from the resonant collision between a breather and two dark line solitons. The limit case of a rogue breather is a rogue lump, which is truly localized in time and in the two-dimensional space. The Nth-order rogue lumps on a background of (N+1) dark line solitons are constructed by employing the Kadomtsev-Petviashvili hierarchy reduction method combined with the Hirota bilinear method. These higher-order lumps arise from a background of dark line solitons and then disappear into the background again after living for a very short period of time. The rogue lumps possess the key features of two-dimensional rogue waves occurring in a plethora of physical settings.

Observation of modulation instability and rogue breathers on stationary periodic waves

We present both theoretical description and experimental observation of the modulation instability process and related rogue breathers in the case of stationary periodic background waves, namely cnoidal and dnoidal envelopes. Despite being well-known solutions of the nonlinear Schrodinger equation, the stability of such background waves has remained unexplored experimentally until now, unlike the fundamental plane wave. By means of two experimental setups, namely, in nonlinear optics and hydrodynamics, we report on quantitative measurements of spontaneous modulation instability gain seeded by input random noise, as well as the formation of rogue breather solutions induced by a coherent perturbation. Our results confirm the generalization of modulation instability when more complex background waves are involved.

Rogue breather modes: Topological sectors, and the ‘belt-trick’, in a one-dimensional ferromagnetic spin chain

We present explicit solutions for breather soliton modes of excitation in the one-dimensional Heisenberg ferromagnetic spin chain. We identify a characteristic geometrical feature of these breather modes wherein a helicoidal configuration of spins is continuously transformed to one which differs from the initial helicoid by a total twist of `2'. This is a curious manoeuvre popularly known as the `belt trick', an illustration of the simple connectedness of the $\rm{SU}(2)$ group manifold, and its rotation period $4\pi$. We show that this effectively splits the configuration space of the ferromagnetic chain in one-dimension into two topological sectors, distinguished by their total twist -- either `0', or `1'. Further, the energy lower bound of the two sectors is separated by a finite gap varying inversely with the size of the lattice.