About this Research Topic

Background

This Research Topic commemorates the 10th anniversary of the observation of Peregrine soliton.

Nonlinearity plays an essential role in scientific research, including the understanding of natural phenomena and the development of advanced technologies. The nonlinear Schrödinger equation (NLSE) in its many forms serves as a key model in many different areas of physics, and more specifically in nonlinear wave theory. Exciting and fascinating nonlinear phenomena, such as the modulation instability process and propagation of envelope solitons, have been pioneered by numerous theoretical, numerical and particularly experimental studies in the second half of the 20th century. At the present time, its versatility includes a large range of research fields, such as deep and finite depth water, plasmas, laser light, electrical transmission lines, and Bose-Einstein condensates.

More recently, the emerging field of rogue wave physics has completely revolutionized this landscape, since the study of extreme wave generation has been extended well beyond the usual hydrodynamics community, in particular, due to the analogy drawn through the NLSE and related nonlinear wave theory. Indeed, one could expect to address the issue of rogue waves within the framework of NLSE breather solutions whose entire space-time evolution is analytically described. Their pulsating and localization properties made such unstable waves as the simplest nonlinear prototypes of well-known hydrodynamic rogue waves. More specifically, the limiting case of infinite modulation period, namely the Peregrine soliton is doubly localized in both, space and time. Analytically derived in the early ’80s by D. Howell Peregrine, it has remained untested experimentally for almost 30 years. Following the observation in nonlinear optics, the possibility of generation or emergence of the Peregrine soliton in other real physical systems was shown.

The proof of existence and control of this untested class of nonlinear waves has been of fundamental importance since it now drives numerous experimental studies in various systems, as well as mathematical developments, worldwide. It has also revealed important technical and fundamental issues related to open questions and challenges in wave physics that are still under investigation and even under debate, such as the impact of dissipation or higher-dimensional effects, the improvement of fast spatiotemporal measurements, the predictability of rogue waves, the understanding of wave turbulence, to cite only a few.

This Research Topic calls for Original Research, Review, Brief Research Report, Mini Review, and Perspective articles dealing with achievements or perspectives, and based on theoretical, numerical, and experimental studies of modulation instability processes and related breather waves, including the famous Peregrine soliton and other rogue wave solutions. Overall, this interdisciplinary topic is expected to further strengthen interactions and bonds between disciplines connected to the physics of nonlinear waves.

Keywords: Breather solutions, Nonlinear Schrödinger equation, Nonlinear waves, Modulation instability, Rogue waves

Important note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.

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