Higher-order rogue wave solutions of the three-wave resonant interaction equation via the generalized Darboux transformation

2015 ◽  
Vol 90 (10) ◽  
pp. 105201 ◽  
Author(s):  
Xin Wang ◽  
Jianli Cao ◽  
Yong Chen
Keyword(s):  
Darboux Transformation ◽  
Rogue Wave ◽  
Resonant Interaction ◽  
Higher Order ◽  
Wave Solutions ◽  
Interaction Equation ◽  
Generalized Darboux Transformation ◽  
Rogue Wave Solutions

Generalized Darboux transformation and higher-order rogue wave solutions to the Manakov system

2021 ◽  
Author(s):  
Serge P. Mukam ◽  
Souleymanou Abbagari ◽  
Alphonse Houwe ◽  
Victor K. Kuetche ◽  
Mustafa Inc ◽  
...  
Keyword(s):  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Rogue Wave ◽  
Higher Order ◽  
Lax Pairs ◽  
Wave Solutions ◽  
Free Parameters ◽  
Generalized Darboux Transformation ◽  
Rogue Wave Solutions ◽  
Physical Phenomena

In this paper, we propose a recursive Darboux transformation in a generalized form of a focusing vector Nonlinear Schrödinger Equation (NLSE) known as the Manakov System. We apply this generalized recursive Darboux transformation to the Lax-pairs of this system in view of generating the Nth-order vector generalization rogue wave solutions with a rule of iteration. We discuss from first- to three-order vector generalizations of rogue wave solutions while illustrating these features with some 3D, 2D graphical depictions. We illustrate a clear connection between higher-order rogue wave solutions and their free parameters for better understanding the physical phenomena described by the Manakov system

scholarly journals Rogue Wave Solutions and Generalized Darboux Transformation for an Inhomogeneous Fifth-Order Nonlinear Schrödinger Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
N. Song ◽  
W. Zhang ◽  
P. Wang ◽  
Y. K. Xue
Keyword(s):  
Darboux Transformation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Wave Solutions ◽  
Generalized Darboux Transformation ◽  
Rogue Wave Solutions ◽  
Fifth Order

The rogue wave solutions are discussed for an inhomogeneous fifth-order nonlinear Schrödinger equation, which describes the dynamics of a site-dependent Heisenberg ferromagnetic spin chain. Using the Darboux matrix, the generalized Darboux transformation is constructed and a recursive formula is derived. Based on the transformation, the first-order to the third-order rogue wave solutions are obtained. Then, the nonlinear dynamics of the first-order to the third-order rogue waves are studied on the basis of some free parameters. Several new structures of the rogue waves are found using numerical simulation. The conclusions will be a supportive tool to study the rogue waves better.

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