On quasi-periodic waves and rogue waves to the (4+1)-dimensional nonlinear Fokas equation

2018 ◽  
Vol 59 (7) ◽  
pp. 073505 ◽  
Author(s):  
Xiu-Bin Wang ◽  
Shou-Fu Tian ◽  
Lian-Li Feng ◽  
Tian-Tian Zhang
Keyword(s):  
Rogue Waves ◽  
Periodic Waves

Rogue waves in multiple-solitons–inelastic collisions — The complex Sharma–Tasso–Olver equation

2018 ◽  
Vol 32 (08) ◽  
pp. 1750360 ◽  
Author(s):  
H. I. Abdel-Gawad ◽  
M. Tantawy
Keyword(s):  
Spectral Band ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Inelastic Collisions ◽  
Periodic Waves ◽  
Mechanism Of Formation ◽  
Free Parameters ◽  
Generalized Unified Method ◽  
The Generalized Unified Method ◽  
Unified Method

Very recently, a mechanism to the formation of rogue waves (RWs) has been proposed by the authors. In this paper, the formation of RWs in case of the complex Sharma–Tasso–Olver (STO) equation is studied. In the STO equation, one, two and three-soliton solutions are obtained. Due to the inelastic collisions, these soliton waves are fused to one. Under the free parameters constraint this behavior do occurs. The mechanism of formation of RWs is due to the collisions of solitons and multi-periodic waves (like spectral band). These RWs as giant waves, which may be very sharp or chaotic are similar to RWs in laser. The work is done here by using the generalized unified method (GUM).

scholarly journals Rogue waves on the general periodic travelling waves background for an extended modified Korteweg-de Vries equation

2021 ◽  
Author(s):  
Yi Zhang ◽  
Yu Lou ◽  
RS Ye
Keyword(s):  
Vries Equation ◽  
Travelling Waves ◽  
Three Dimensional ◽  
Rogue Waves ◽  
Travelling Wave ◽  
Periodic Waves ◽  
Travelling Wave Solutions ◽  
Third Order ◽  
Periodic Travelling Wave ◽  
De Vries

Under consideration in this paper is rogue waves on the general periodic travelling waves background of an integrable extended modified Korteweg-de Vries equation. The general periodic travelling wave solutions are presented in terms of the sub-equation method. By means of the Darboux transformation and the nonlinearization of the Lax pair, we present the first-, second- and third-order rogue waves on the general periodic travelling waves background. Furthermore, the dynamic behaviors of rogue periodic waves are elucidated from the viewpoint of three-dimensional structures.

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
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