General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation
By Yasuhiro Ohta, Jianke Yang. Proceedings of the Royal Society A, 2011
513 citations recorded by the source corpus.
General high-order rogue waves in the nonlinear Schrödinger equation are derived by the bilinear method. These rogue waves are given in terms of determinants whose matrix elements have simple algebraic expressions. It is shown that the general N-th order rogue waves contain N−1 free irreducible complex parameters. In addition, the specific rogue waves obtained by Akhmediev et al. (Akhmediev et al. 2009 Phys. Rev. E 80, 026601 (doi:10.1103/PhysRevE.80.026601)) correspond to special choices of these free parameters, and they have the highest peak amplitudes among all rogue waves of the same order. If other values of these free parameters are taken, however, these general rogue waves can exhibit other solution dynamics such as arrays of fundamental rogue waves arising at different times and spatial positions and forming interesting patterns.
Subfields: Modeling and Simulation, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/6f17a9d5e95825dd36c2fdeb0365960b320fde70
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In Modeling and Simulation
In Statistical and Nonlinear Physics
- Sergei K. Turitsyn
- Jianke Yang
- John M. Dudley
- Dmitry A. Zezyulin
- Nail Akhmediev
- Daniel Solli
- Vladimir V. Konotop
- Boris A. Malomed
Citations in the corpus
- Recent progress in investigating optical rogue waves (2013, background): “Generally, multi-parameter higher-order rogue wave solutions can be revealed in a variety of other regular shapes [89, 90].”
- Novel high‐order breathers and rogue waves in the Boussinesq equation via determinants (2019, unknown): “with ζ1 = −ω1x + 2iω1Ω1t + ζ0 1 ,A12 = (Ω1 + Ω1) 2 (Ω1 + Ω1)(2) − ω 2 1 , (21)”
- Nonlinear waves in PT -symmetric systems (2016, background): “They 38 can be readily obtained from higher-order rogue waves of the NLS equation through the reduction (109)–(110) (Akhmediev, Ankiewicz, and Soto-Crespo, 2009; Dai and Huang, 2014; Dubard et al., 2010; Guo, Ling, and Liu, 2012; Ohta and Yang, 2012).”