Discrete Rogue Waves

This Demonstration shows the development of a discrete rogue wave according to the commonly used Ablowitz–Ladik equation: . As one application, such a wave can model light propagation in strongly interacting parallel optical waveguides. The amplitude, , is defined only at a discrete set of sites (), although the propagation variable is continuous.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


A rogue wave is a unique event that occurs when a disturbance builds up on a constant background to form a high amplitude part, but later decreases into the background. This Demonstration illustrates the curious fact that rogue waves can exist in discrete systems, for example in an array of optical waveguides. Thus they are analogous to those in continuous systems, like the nonlinear Schrödinger equation (NLSE). Rogue waves arise as solutions of the Ablowitz–Ladik system, even though this is not a direct discretization of the NLSE.
Waves of the two lowest orders are shown here. You can switch from one to the other by clicking "basic" or "second order". You can also change the distance of propagation and observe the rise of the central part above the background when the distance, , approaches zero. The maximum can indeed be much higher than the other nearby sites. When the offset is 1/2 or -1/2, then the two central heights are equal.
For more details, see A. Ankiewicz, N. Akhmediev, and J. M. Soto-Crespo, "Discrete Rogue Waves of the Ablowitz-Ladik and Hirota Equations," Physical Review E 82, 2010. DOI: 10.1103/PhysRevE.82.026602.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+