Continuous-discrete duality of the nonlinear Schrödinger and Ablowitz–Ladik rogue wave hierarchies

2017 ◽  
pp. 79-96
Author(s):  
A. Ankiewicz ◽  
D.J. Kedziora ◽  
N. Akhmediev
Keyword(s):  
Rogue Wave ◽  
Nonlinear Schrödinger

New Rational Homoclinic Solution and Rogue Wave Solution for the Coupled Nonlinear Schrödinger Equation

2014 ◽  
Vol 69 (8-9) ◽  
pp. 441-445 ◽  
Author(s):  
Long-Xing Li ◽  
Jun Liu ◽  
Zheng-De Dai ◽  
Ren-Lang Liu
Keyword(s):  
Schrödinger Equation ◽  
Wave Solution ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Homoclinic Solution ◽  
Nonlinear Schrodinger Equation ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Coupled Nonlinear Schrödinger Equation ◽  
Rogue Wave Solution

In this work, the rational homoclinic solution (rogue wave solution) can be obtained via the classical homoclinic solution for the nonlinear Schrödinger (NLS) equation and the coupled nonlinear Schrödinger (CNLS) equation, respectively. This is a new way for generating rogue wave comparing with direct constructing method and Darboux dressing technique

Breather and rogue wave solutions for a nonlinear Schrödinger-type system in plasmas

2015 ◽  
Vol 81 (1-2) ◽  
pp. 739-751 ◽  
Author(s):  
Gao-Qing Meng ◽  
Jin-Lei Qin ◽  
Guo-Liang Yu
Keyword(s):  
Rogue Wave ◽  
Type System ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Rogue Wave Solutions

The rogue wave of the nonlinear Schrödinger equation with self-consistent sources

2018 ◽  
Vol 32 (30) ◽  
pp. 1850367 ◽  
Author(s):  
Yehui Huang ◽  
Hongqing Jing ◽  
Runliang Lin ◽  
Yuqin Yao
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Wave Solution ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Breather Solution ◽  
Rogue Wave Solution ◽  
Self Consistent

In this paper, we study the nonlinear Schrödinger equation with self-consistent sources, and obtain the rogue wave solution, the breather solution and their interactions by the generalized Darboux transformation. The dynamics of the rogue wave solution, the breather solution and their interactions are analyzed.

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