Directional Soliton and Breather Beams

The modulation instability is a focusing mechanism responsible for the formation of strong wave localizations not only on the water surface, but also in a variety of nonlinear dispersive media. Such dynamics is initiated from the injection of side-bands, which translate into an amplitude modulation of the wave field. The nonlinear stage of unstable wave evolution can be described by exact solutions of the nonlinear Schr\"odinger equation (NLSE). In that case, the amplitude mo...

Being considered as a prototype for description of oceanic rogue waves (RWs), the Peregrine breather solution of the nonlinear Schr\"odinger equation (NLS) has been recently observed and intensely investigated experimentally in particular within the context of water waves. Here, we report the experimental results showing the evolution of the Peregrine solution in the presence of wind forcing in the direction of wave propagation. The results show the persistence of the breathe...

We consider the evolution of the 2-soliton (breather) of the nonlinear Schroedinger equation on a semi-infinite line with the zero boundary condition and a linear potential, which corresponds to the gravity field in the presence of a hard floor. This setting can be implemented in atomic Bose-Einstein condensates, and in a nonlinear planar waveguide in optics. In the absence of the gravity, repulsion of the breather from the floor leads to its splitting into constituent fundam...

We describe laboratory experiments in a 2D wave tank that aim at building up and monitor 2D shallow water soliton gas. The water surface elevation is obtained over a large ($\sim 100\,\text{m}^2$) domain, with centimetre-resolution, by stereoscopic vision using two cameras. Floating particles are seeded to get surface texture and determine the wave field by image correlation. With this set-up, soliton propagation and multiple interactions can be measured with a previously unr...

In this paper, we present the two-dimensional generalized nonlinear Schr\"odinger equations with the Lax pair. These equations are related to many physical phenomena in the Bose-Einstein condensates, surface waves in deep water and nonlinear optics. The existence of the Lax pair defines integrability for the partial differential equation, so the two-dimensional generalized nonlinear Schr\"odinger equations are integrable. We obtain bilinear forms of the two-dimensional GNLS e...

The generation of finite energy packets of X-waves is analysed in normally dispersive cubic media by using an X-wave expansion. The 3D nonlinear Schroedinger model is reduced to a 1D equation with anomalous dispersion. Pulse splitting and beam replenishment as observed in experiments with water and Kerr media are explained in terms of a higher order breathing soliton. The results presented also hold in periodic media and Bose-condensed gases.

We investigate the Zeno dynamics of the optical rogue waves. Considering their usage in modeling rogue wave dynamics, we analyze the Zeno dynamics of the Akhmediev breathers, Peregrine and Akhmediev-Peregrine soliton solutions of the nonlinear Schrodinger equation. We show that frequent measurements of the wave inhibits its movement in the observation domain for each of these solutions. We analyze the spectra of the rogue waves under Zeno dynamics. We also analyze the effect ...

Solitons, the distinct balance between nonlinearity and dispersion, provide a route toward ultrafast electromagnetic pulse shaping, high-harmonic generation, real-time image processing, and RF photonic communications. Here we newly explore and observe the spatio-temporal breather dynamics of optical soliton crystals in frequency microcombs, examining spatial breathers, chaos transitions, and dynamical deterministic switching in nonlinear measurements and theory. To understand...

Ocean waves are complex and often turbulent. While most ocean wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much taller than the sum of the original wave heights. Most of these nonlinear interactions look like an X or a Y or two connected Ys; at other times, several lines appear on each side of the interaction region. It was thought that such nonlinear int...

We introduce a dynamic stabilization scheme universally applicable to unidirectional nonlinear coherent waves. By abruptly changing the waveguiding properties, the breathing of wave packets subject to modulation instability can be stabilized as a result of the abrupt expansion a homoclinic orbit and its fall into an elliptic fixed point (center). We apply this concept to the nonlinear Schr\"odinger equation framework and show that an Akhmediev breather envelope, which is at t...