scholarly journals Dissipative Light Bullets in Kerr Cavities: Multistability, Clustering, and Rogue Waves

2021 ◽  
Vol 126 (15) ◽  
Author(s):  
S. S. Gopalakrishnan ◽  
K. Panajotov ◽  
M. Taki ◽  
M. Tlidi
Keyword(s):  
Rogue Waves ◽  
Light Bullets

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.

scholarly journals Two-dimensional rogue waves on zero background in a Benney-Roskes model

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Lijuan Guo ◽  
Jingsong He ◽  
Lihong Wang ◽  
Yi Cheng ◽  
D. J. Frantzeskakis ◽  
...  
Keyword(s):  
Rogue Waves ◽  
Two Dimensional

Modeling internal rogue waves in a long wave-short wave resonance framework

2018 ◽  
Vol 3 (12) ◽  
Author(s):  
H. N. Chan ◽  
R. H. J. Grimshaw ◽  
K. W. Chow
Keyword(s):  
Rogue Waves ◽  
Short Wave ◽  
Long Wave ◽  
Wave Resonance

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.

scholarly journals On the physical constraints for the exceeding probability of deep water rogue waves

2021 ◽  
Vol 108 ◽  
pp. 102402
Author(s):  
S. Mendes ◽  
A. Scotti ◽  
P. Stansell
Keyword(s):  
Deep Water ◽  
Rogue Waves ◽  
Physical Constraints
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