Darboux transformation and dark rogue wave states arising from two-wave resonance interaction

2014 ◽  
Vol 378 (16-17) ◽  
pp. 1095-1098 ◽  
Author(s):  
Shihua Chen
Keyword(s):  
Darboux Transformation ◽  
Rogue Wave ◽  
Resonance Interaction ◽  
Wave Resonance ◽  
Wave States

Application of the Weierstrass Elliptic Expansion Method to the Long-Wave and Short-Wave Resonance Interaction System

2008 ◽  
Vol 63 (5-6) ◽  
pp. 273-279 ◽  
Author(s):  
Xian-Jing Lai ◽  
Jie-Fang Zhang ◽  
Shan-Hai Mei
Keyword(s):  
Periodic Solutions ◽  
Elliptic Function ◽  
Expansion Method ◽  
Short Wave ◽  
Resonance Interaction ◽  
Solitary Wave Solutions ◽  
Jacobian Elliptic Function ◽  
Weierstrass Elliptic Function ◽  
Long Wave ◽  
Wave Resonance

With the aid of symbolic computation, nine families of new doubly periodic solutions are obtained for the (2+1)-dimensional long-wave and short-wave resonance interaction (LSRI) system in terms of the Weierstrass elliptic function method. Moreover Jacobian elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.

scholarly journals General rogue wave solutions of the coupled Fokas–Lenells equations and non-recursive Darboux transformation

2019 ◽  
Vol 475 (2224) ◽  
pp. 20180806 ◽  
Author(s):  
Yanlin Ye ◽  
Yi Zhou ◽  
Shihua Chen ◽  
Fabio Baronio ◽  
Philippe Grelu
Keyword(s):  
Darboux Transformation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Background Field ◽  
Double Root ◽  
Transformation Technique ◽  
Wave Dynamics ◽  
Wave Solutions ◽  
Future Experimental Study ◽  
Rogue Wave Solutions

We formulate a non-recursive Darboux transformation technique to obtain the general n th-order rational rogue wave solutions to the coupled Fokas–Lenells system, which is an integrable extension of the noted Manakov system, by considering both the double-root and triple-root situations of the spectral characteristic equation. Based on the explicit fundamental and second-order rogue wave solutions, we demonstrate several interesting rogue wave dynamics, among which are coexisting rogue waves and anomalous Peregrine solitons. Our solutions are generalized to include the complete background-field parameters and therefore helpful for future experimental study.

scholarly journals Dynamics of solitons in multicomponent long wave–short wave resonance interaction system

Pramana ◽  
2015 ◽  
Vol 84 (3) ◽  
pp. 327-338 ◽  
Author(s):  
T KANNA ◽  
K SAKKARAVARTHI ◽  
M VIJAYAJAYANTHI ◽  
M LAKSHMANAN
Keyword(s):  
Short Wave ◽  
Resonance Interaction ◽  
Long Wave ◽  
Interaction System ◽  
Wave Resonance

scholarly journals Rogue Wave Modes for the Long Wave–Short Wave Resonance Model

2013 ◽  
Vol 82 (7) ◽  
pp. 074001 ◽  
Author(s):  
Kwok Wing Chow ◽  
Hiu Ning Chan ◽  
David Jacob Kedziora ◽  
Roger Hamilton James Grimshaw
Keyword(s):  
Rogue Wave ◽  
Short Wave ◽  
Resonance Model ◽  
Long Wave ◽  
Wave Resonance ◽  
Wave Modes

Rogue wave solutions for the higher-order nonlinear Schrödinger equation with variable coefficients by generalized Darboux transformation

2016 ◽  
Vol 30 (10) ◽  
pp. 1650106 ◽  
Author(s):  
Hai-Qiang Zhang ◽  
Jian Chen
Keyword(s):  
Darboux Transformation ◽  
Variable Coefficient ◽  
Rogue Wave ◽  
Variable Coefficients ◽  
Higher Order ◽  
Optical Systems ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Order Variable ◽  
Generalized Darboux Transformation

In this paper, we study a higher-order variable coefficient nonlinear Schrödinger (NLS) equation, which plays an important role in the control of the ultrashort optical pulse propagation in nonlinear optical systems. Then, we construct a generalized Darboux transformation (GDT) for the higher-order variable coefficient NLS equation. The [Formula: see text]th order rogue wave solution is obtained by the iterative rule and it can be expressed by the determinant form. As application, we calculate rogue waves (RWs) from first- to fourth-order in accordance with different kinds of parameters. In particular, the dynamical properties and spatial-temporal structures of RWs are discussed and compared with Hirota equation through some figures.

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