Rational solitary wave and rogue wave solutions in coupled defocusing Hirota equation

2016 ◽  
Vol 380 (25-26) ◽  
pp. 2136-2141 ◽  
Author(s):  
Xin Huang
Keyword(s):  
Solitary Wave ◽  
Rogue Wave ◽  
Hirota Equation ◽  
Wave Solutions ◽  
Rogue Wave Solutions

Deformed soliton, breather and rogue wave solutions of an inhomogeneous nonlinear Hirota equation

2015 ◽  
Vol 29 (1-3) ◽  
pp. 257-266 ◽  
Author(s):  
Xiaotong Liu ◽  
Xuelin Yong ◽  
Yehui Huang ◽  
Rui Yu ◽  
Jianwei Gao
Keyword(s):  
Rogue Wave ◽  
Hirota Equation ◽  
Wave Solutions ◽  
Rogue Wave Solutions

Rogue Waves and New Multi-wave Solutions of the (2+1)-Dimensional Ito Equation

2015 ◽  
Vol 70 (6) ◽  
pp. 437-443 ◽  
Author(s):  
Ying-hui Tian ◽  
Zheng-de Dai
Keyword(s):  
Solitary Wave ◽  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Extreme Form ◽  
Wave Solutions ◽  
Rogue Wave Solutions ◽  
Ito Equation

AbstractA three-soliton limit method (TSLM) for seeking rogue wave solutions to nonlinear evolution equation (NEE) is proposed. The (2+1)-dimensional Ito equation is used as an example to illustrate the effectiveness of the method. As a result, two rogue waves and a family of new multi-wave solutions are obtained. The result shows that rogue wave can be obtained not only from extreme form of breather solitary wave but also from extreme form of double-breather solitary wave. This is a new and interesting discovery.

The twin properties of rogue waves and homoclinic solutions for some nonlinear wave equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wei Tan ◽  
Zhao-Yang Yin
Keyword(s):  
Differential Equations ◽  
Wave Equations ◽  
Rogue Wave ◽  
Nonlinear Partial Differential Equations ◽  
Rogue Waves ◽  
Homoclinic Solutions ◽  
Nonlinear Wave Equations ◽  
Bilinear Method ◽  
Wave Solutions ◽  
Rogue Wave Solutions

Abstract The parameter limit method on the basis of Hirota’s bilinear method is proposed to construct the rogue wave solutions for nonlinear partial differential equations (NLPDEs). Some real and complex differential equations are used as concrete examples to illustrate the effectiveness and correctness of the described method. The rogue waves and homoclinic solutions of different structures are obtained and simulated by three-dimensional graphics, respectively. More importantly, we find that rogue wave solutions and homoclinic solutions appear in pairs. That is to say, for some NLPDEs, if there is a homoclinic solution, then there must be a rogue wave solution. The twin phenomenon of rogue wave solutions and homoclinic solutions of a class of NLPDEs is discussed.

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