Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems

Year: 2017

Authors: Chen SH., Baronio F., Soto-Crespo JM., Grelu P., Mihalache D.

Autors Affiliation: Southeast Univ, Dept Phys, Nanjing 211189, Jiangsu, Peoples R China; Univ Brescia, INO CNR, Via Branze 38, I-25123 Brescia, Italy; Univ Brescia, Dipartimento Ingn Informaz, Via Branze 38, I-25123 Brescia, Italy;‎ CSIC, IO, Serrano 121, Madrid 28006, Spain;‎ Univ Bourgogne Franche Comte, Lab ICB, UMR CNRS 6303, 9 Ave A Savary, F-21078 Dijon, France; Horia Hulubei Natl Inst Phys & Nucl Engn, Dept Theoret Phys, RO-077125 Magurele, Romania

Abstract: This review is dedicated to recent progress in the active field of rogue waves, with an emphasis on the analytical prediction of versatile rogue wave structures in scalar, vector, and multidimensional integrable nonlinear systems. We first give a brief outline of the historical background of the rogue wave research, including referring to relevant up-to-date experimental results. Then we present an in-depth discussion of the scalar rogue waves within two different integrable frameworks-the infinite nonlinear Schrodinger (NLS) hierarchy and the general cubic-quintic NLS equation, considering both the self-focusing and self-defocusing Kerr nonlinearities. We highlight the concept of chirped Peregrine solitons, the baseband modulation instability as an origin of rogue waves, and the relation between integrable turbulence and rogue waves, each with illuminating examples confirmed by numerical simulations. Later, we recur to the vector rogue waves in diverse coupled multicomponent systems such as the long-wave short-wave equations, the three-wave resonant interaction equations, and the vector NLS equations (alias Manakov system). In addition to their intriguing bright-dark dynamics, a series of other peculiar structures, such as coexisting rogue waves, watch-hand-like rogue waves, complementary rogue waves, and vector dark three sisters, are reviewed. Finally, for practical considerations, we also remark on higher-dimensional rogue waves occurring in three closely-related (2 + 1) D nonlinear systems, namely, the Davey-Stewartson equation, the composite (2 + 1) D NLS equation, and the Kadomtsev-Petviashvili I equation. As an interesting contrast to the peculiar X-shaped light bullets, a concept of rogue wave bullets intended for high-dimensional systems is particularly put forward by combining contexts in nonlinear optics.


Volume: 50 (46)      Pages from: 463001-1  to: 463001-78

KeyWords: rogue wave; modulation instability; integrable turbulence
DOI: 10.1088/1751-8121/aa8f00

Citations: 149
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