Multiple rogue wave solutions for a (3+1)-dimensional Hirota bilinear equation

2019 ◽  
Vol 98 ◽  
pp. 184-190 ◽  
Author(s):  
Wenhao Liu ◽  
Yufeng Zhang
Keyword(s):  
Rogue Wave ◽  
Wave Solutions ◽  
Hirota Bilinear Equation ◽  
Rogue Wave Solutions ◽  
Hirota Bilinear ◽  
Bilinear Equation

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 Rational wave solutions to a generalized (2+1)-dimensional Hirota bilinear equation

2020 ◽  
Vol 15 ◽  
pp. 61 ◽  
Author(s):  
K. Hosseini ◽  
M. Mirzazadeh ◽  
M. Aligoli ◽  
M. Eslami ◽  
J.G. Liu
Keyword(s):  
Nonlinear Waves ◽  
Soliton Solutions ◽  
Wave Solutions ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Complexiton Solutions ◽  
Hirota Bilinear Equation ◽  
Different Types ◽  
Hirota Bilinear ◽  
Bilinear Equation

A generalized form of (2+1)-dimensional Hirota bilinear (2D-HB) equation is considered herein in order to study nonlinear waves in fluids and oceans. The present goal is carried out through adopting the simplified Hirota’s method as well as ansatz approaches to retrieve a bunch of rational wave structures from multiple soliton solutions to breather, rational, and complexiton solutions. Some figures corresponding to a series of rational wave structures are provided, illustrating the dynamics of the obtained solutions. The results of the present paper help to reveal the existence of rational wave structures of different types for the 2D-HB equation.

scholarly journals Resonant behavior of multiple wave solutions to a Hirota bilinear equation

2016 ◽  
Vol 72 (5) ◽  
pp. 1225-1229 ◽  
Author(s):  
Li-Na Gao ◽  
Xue-Ying Zhao ◽  
Yao-Yao Zi ◽  
Jun Yu ◽  
Xing Lü
Keyword(s):  
Multiple Wave ◽  
Wave Solutions ◽  
Hirota Bilinear Equation ◽  
Resonant Behavior ◽  
Hirota Bilinear ◽  
Bilinear Equation

scholarly journals Traveling Wave Solutions and Infinite-Dimensional Linear Spaces of Multiwave Solutions to Jimbo-Miwa Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lijun Zhang ◽  
C. M. Khalique
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave System ◽  
Infinite Dimensional ◽  
Wave Solutions ◽  
Hirota Bilinear Equation ◽  
Periodic Traveling Wave ◽  
Multiwave Solutions ◽  
Hirota Bilinear ◽  
Bilinear Equation

The traveling wave solutions and multiwave solutions to (3 + 1)-dimensional Jimbo-Miwa equation are investigated in this paper. As a result, besides the exact bounded solitary wave solutions, we obtain the existence of two families of bounded periodic traveling wave solutions and their implicit formulas by analysis of phase portrait of the corresponding traveling wave system. We derive the exact 2-wave solutions and two families of arbitrary finiteN-wave solutions by studying the linear space of its Hirota bilinear equation, which confirms that the (3 + 1)-dimensional Jimbo-Miwa equation admits multiwave solutions of any order and is completely integrable.

Rogue wave solutions, soliton and rogue wave mixed solution for a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation in fluids

2018 ◽  
Vol 32 (29) ◽  
pp. 1850358 ◽  
Author(s):  
Yu-Lan Ma ◽  
Bang-Qing Li
Keyword(s):  
Rogue Wave ◽  
Mixed Solution ◽  
Polynomial Functions ◽  
Nonlinear Wave Propagation ◽  
Bilinear Transformation ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Rogue Wave Solutions ◽  
Evolution Behavior ◽  
Hirota Bilinear

A generalized (3[Formula: see text]+[Formula: see text]1)-dimensional Kadomtsev–Petviashvili equation is investigated, which can be used to describe nonlinear wave propagation in fluids. Through choosing appropriate polynomial functions in bilinear form derived according Hirota bilinear transformation, one and two rogue wave solutions, and soliton and rogue wave mixed solution are constructed. Furthermore, based on the mixed solution, interaction and evolution behavior between the soliton and rogue wave is discussed. The result shows that the soliton will be gradually swallowing up the rogue wave with the increase of time. During the process, the energy carried by the rogue wave is absorbed by the soliton.

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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