scholarly journals On the rogue wave solution in the framework of a Korteweg–de Vries equation

2021 ◽  
Vol 30 ◽  
pp. 104847
Author(s):  
Wedad Albalawi ◽  
S.A. El-Tantawy ◽  
Alvaro H. Salas
Keyword(s):  
Wave Solution ◽  
Vries Equation ◽  
Rogue Wave ◽  
Rogue Wave Solution ◽  
De Vries

Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huanhuan Lu ◽  
Yufeng Zhang
Keyword(s):  
Vries Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
Wave Solutions ◽  
De Vries ◽  
Rogue Wave Solutions ◽  
Bilinear Formulation ◽  
Hirota Bilinear

AbstractIn this paper, we analyse two types of rogue wave solutions generated from two improved ansatzs, to the (2 + 1)-dimensional generalized Korteweg–de Vries equation. With symbolic computation, the first-order rogue waves, second-order rogue waves, third-order rogue waves are generated directly from the first ansatz. Based on the Hirota bilinear formulation, another type of one-rogue waves and two-rogue waves can be obtained from the second ansatz. In addition, the dynamic behaviours of obtained rogue wave solutions are illustrated graphically.

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.

scholarly journals Rogue Wave for the (3+1)-Dimensional Yu-Toda-Sasa-Fukuyama Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hanlin Chen ◽  
Zhenhui Xu ◽  
Zhengde Dai
Keyword(s):  
Nonlinear Evolution Equation ◽  
Wave Solution ◽  
Nonlinear Evolution ◽  
Rogue Wave ◽  
Test Method ◽  
Wave Fields ◽  
New Family ◽  
Rogue Wave Solution ◽  
Extreme Behavior ◽  
Ytsf Equation

A new method, homoclinic (heteroclinic) breather limit method (HBLM), for seeking rogue wave solution to nonlinear evolution equation (NEE) is proposed. (3+1)-dimensional Yu-Toda-Sasa-Fukuyama (YTSF) equation is used as an example to illustrate the effectiveness of the suggested method. A new family of two-wave solution, rational breather wave solution, is obtained by extended homoclinic test method, and it is just a rogue wave solution. This result shows rogue wave can come from extreme behavior of breather solitary wave for (3+1)-dimensional nonlinear wave fields.

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