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

Journal
Physical review E - Covering statistical, nonlinear, biological, and soft matter physics  
Volume
90
Issue
3
Article Number
032902
Citation
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 90 (3): 032902 (2014-09-02)
Publisher DOI
10.1103/PhysRevE.90.032902
Scopus ID
2-s2.0-84907486807
PubMed ID
25314499
Publisher
American Physical Society
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.
DDC Class
530: Physik
Funding Organisations
Volkswagen Stiftung
Australian Research Council
Alexander von Humboldt-Stiftung  
MINECO
More Funding Information
The authors acknowledge the support from the Volkswagen Stiftung. N.D. and N.A. acknowledge the support of the Australian Research Council (Discovery Project DP140100265). N.A. acknowledges support through the Alexander von Humboldt Award (Germany). The work of J.M.S.C. is supported by the MINECO, under Contracts No. FIS2009- 09895 and No. TEC2012-37958-C02-02.