Rogue waves of the Sasa-Satsuma equation in a chaotic wave field

J. M. Soto-Crespo; N. Devine; N. P. Hoffmann; N. Akhmediev

doi:10.1103/PhysRevE.90.032902

Rogue waves of the Sasa-Satsuma equation in a chaotic wave field

J. M. Soto-Crespo^*, N. Devine, N. P. Hoffmann, N. Akhmediev

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

50 Citations (Scopus)

Abstract

We study the properties of the chaotic wave fields generated in the frame of the Sasa-Satsuma equation (SSE). Modulation instability results in a chaotic pattern of small-scale filaments with a free parameter - the propagation constant k. The average velocity of the filaments is approximately given by the group velocity calculated from the dispersion relation for the plane-wave solution. Remarkably, our results reveal the reason for the skewed profile of the exact SSE rogue-wave solutions, which was one of their distinctive unexplained features. We have also calculated the probability density functions for various values of the propagation constant k, showing that probability of appearance of rogue waves depends on k.

Original language	English
Article number	032902
Journal	Physical Review E
Volume	90
Issue number	3
DOIs	https://doi.org/10.1103/PhysRevE.90.032902
Publication status	Published - 2 Sept 2014

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title = "Rogue waves of the Sasa-Satsuma equation in a chaotic wave field",

abstract = "We study the properties of the chaotic wave fields generated in the frame of the Sasa-Satsuma equation (SSE). Modulation instability results in a chaotic pattern of small-scale filaments with a free parameter - the propagation constant k. The average velocity of the filaments is approximately given by the group velocity calculated from the dispersion relation for the plane-wave solution. Remarkably, our results reveal the reason for the skewed profile of the exact SSE rogue-wave solutions, which was one of their distinctive unexplained features. We have also calculated the probability density functions for various values of the propagation constant k, showing that probability of appearance of rogue waves depends on k.",

author = "Soto-Crespo, {J. M.} and N. Devine and Hoffmann, {N. P.} and N. Akhmediev",

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AU - Akhmediev, N.

PY - 2014/9/2

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N2 - We study the properties of the chaotic wave fields generated in the frame of the Sasa-Satsuma equation (SSE). Modulation instability results in a chaotic pattern of small-scale filaments with a free parameter - the propagation constant k. The average velocity of the filaments is approximately given by the group velocity calculated from the dispersion relation for the plane-wave solution. Remarkably, our results reveal the reason for the skewed profile of the exact SSE rogue-wave solutions, which was one of their distinctive unexplained features. We have also calculated the probability density functions for various values of the propagation constant k, showing that probability of appearance of rogue waves depends on k.

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Rogue waves of the Sasa-Satsuma equation in a chaotic wave field

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