2 research outputs found
Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems
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 Schrödinger (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 (aliasManakov system). In addition to their intriguing bright–dark dynamics,
a series of other peculiar structures, such as coexisting rogue waves, watchhand-
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