scholarly journals Multiple rogue wave solutions for the generalized (2+1)-dimensional Camassa–Holm-Kadomtsev–Petviashvili equation

2021 ◽  
Author(s):  
Jian-Guo Liu ◽  
Huan Zhao
Keyword(s):  
Rogue Wave ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Rogue Wave Solutions

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.

Multiple-order line rogue wave solutions of extended Kadomtsev–Petviashvili equation

2021 ◽  
Vol 180 ◽  
pp. 251-257 ◽  
Author(s):  
Jutong Guo ◽  
Jingsong He ◽  
Maohua Li ◽  
Dumitru Mihalache
Keyword(s):  
Rogue Wave ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Rogue Wave Solutions ◽  
Order Line

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.

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.

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