Generalized Darboux transformation and rogue wave solution of the coherently-coupled nonlinear Schrödinger system

2016 ◽  
Vol 30 (13) ◽  
pp. 1650208 ◽  
Author(s):  
Hai-Qiang Zhang ◽  
Sha-Sha Yuan ◽  
Yue Wang
Keyword(s):  
Darboux Transformation ◽  
Wave Solution ◽  
Rogue Wave ◽  
Rogue Waves ◽  
First Order ◽  
Nonlinear Schrödinger ◽  
Rogue Wave Solution ◽  
Bright Soliton Solution ◽  
Generalized Darboux Transformation ◽  
Schrödinger System

In this paper, the generalized Darboux transformation for the coherently-coupled nonlinear Schrödinger (CCNLS) system is constructed in terms of determinant representations. Based on the Nth-iterated formula, the vector bright soliton solution and vector rogue wave solution are systematically derived under the nonvanishing background. The general first-order vector rogue wave solution can admit many different fundamental patterns including eye-shaped and four-petaled rogue waves. It is believed that there are many more abundant patterns for high order vector rogue waves in CCNLS 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.

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

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.

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.

scholarly journals Novel Particular Solutions, Breathers, and Rogue Waves for an Integrable Nonlocal Derivative Nonlinear Schrödinger Equation

2022 ◽  
Vol 2022 ◽  
pp. 1-9
Author(s):  
Yali Shen ◽  
Ruoxia Yao
Keyword(s):  
Darboux Transformation ◽  
Taylor Expansion ◽  
Rogue Wave ◽  
Rogue Waves ◽  
First Order ◽  
Particular Solutions ◽  
Wave Solutions ◽  
Determinant Representation ◽  
Derivative Nonlinear Schrödinger Equation ◽  
Dnls Equation

A determinant representation of the n -fold Darboux transformation for the integrable nonlocal derivative nonlinear Schödinger (DNLS) equation is presented. Using the proposed Darboux transformation, we construct some particular solutions from zero seed, which have not been reported so far for locally integrable systems. We also obtain explicit breathers from a nonzero seed with constant amplitude, deduce the corresponding extended Taylor expansion, and obtain several first-order rogue wave solutions. Our results reveal several interesting phenomena which differ from those emerging from the classical DNLS equation.

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