# Rogue waves in nonlocal media.

@article{Horikis2017RogueWI, title={Rogue waves in nonlocal media.}, author={Theodoros P. Horikis and Mark J. Ablowitz}, journal={Physical review. E}, year={2017}, volume={95 4-1}, pages={ 042211 } }

The generation of rogue waves is investigated in a class of nonlocal nonlinear Schrödinger (NLS) equations. In this system, modulation instability is suppressed as the effect of nonlocality increases. Despite this fact, there is a parameter regime where the number and amplitude of the rogue events increase as compared to the standard NLS equation, which is a limit of the system when nonlocality vanishes. Furthermore, the nature of these waves is investigated; while no analytical solutions are… Expand

#### 6 Citations

Rogue waves and periodic solutions of a nonlocal nonlinear Schrödinger model

- Physics
- 2020

In the present work, a nonlocal nonlinear Schr\"odinger (NLS) model is studied by means of a recent technique that identifies solutions of partial differential equations, by considering them as fixed… Expand

Rational and semi-rational solutions of the y-nonlocal Davey-Stewartson I equation

- Mathematics, Computer Science
- Comput. Math. Appl.
- 2018

It is shown that a family of hybrid solitons describing the Peregrine rogue wave that coexists with the Akhmediev breather, both of them sitting on a spatially-periodic background can be thus obtained. Expand

Integrability, Darboux transformation and exact solutions for nonlocal couplings of AKNS equations

- Computer Science, Mathematics
- Appl. Math. Lett.
- 2021

The construction of nonlocal equations shows that the symmetry reduction method can not only construct a single nonlocal equation, but also can construct a set of equations. Expand

Semi-rational solutions of the third-type Davey-Stewartson equation.

- Physics, Mathematics
- Chaos
- 2017

These semi-rational solutions consisting of rogue waves, breathers, and solitons are given in terms of determinants whose matrix elements have simple algebraic expressions and have a new phenomenon: lumps form on darksolitons and gradual separation from the dark sol itons is observed. Expand

Multiphase solutions of nonlocal symmetric reductions of equations of the AKNS hierarchy: General analysis and simplest examples

- Mathematics
- 2020

We consider nonlocal symmetries that all or all even (all odd) equations of the AKNS hierarchy have. We construct examples of solutions simultaneously satisfying several nonlocal equations of the… Expand

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