scholarly journals Multi‐breather and high‐order rogue waves for the nonlinear Schrödinger equation on the elliptic function background

2019 ◽  
Vol 144 (1) ◽  
pp. 46-101 ◽  
Author(s):  
Bao‐Feng Feng ◽  
Liming Ling ◽  
Daisuke A. Takahashi
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Elliptic Function ◽  
Schrodinger Equation ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
High Order ◽  
Nonlinear Schrödinger

scholarly journals General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation

2012 ◽  
Vol 468 (2142) ◽  
pp. 1716-1740 ◽  
Author(s):  
Yasuhiro Ohta ◽  
Jianke Yang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
High Order ◽  
Bilinear Method ◽  
Nonlinear Schrödinger ◽  
Solution Dynamics ◽  
Free Parameters

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.

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