研究目的
To review the different dynamical mechanisms leading to the emergence of coherent structures in physical systems described by the integrable one-dimensional nonlinear Schr?dinger equation (1DNLSE) in the focusing regime, with a focus on one-dimensional optical experiments and particularly on optical fibers experiments.
研究成果
The review highlights the rich dynamics of the 1DNLSE in optical fibers, including the emergence of rogue waves through modulation instability and self-focusing. It underscores the importance of initial conditions in determining the system's evolution and the role of integrable turbulence in understanding the statistical properties of nonlinear random waves. The paper also points out the challenges in fully understanding the statistical features of nonlinear random waves in integrable systems and suggests future research directions, including the influence of high-order effects and losses.
研究不足
The review is limited to phenomena described by the integrable 1DNLSE, acknowledging that real experiments may involve additional effects like higher order dispersion, dissipation, and Raman scattering which break integrability. The focus is primarily on one-dimensional optical systems, particularly single-mode fibers.