scholarly journals Two kinds of breather solitary wave and rogue wave solutions for the (3+1)-dimensional Kadomtsev-Petviashvili equation

2017 ◽  
Vol 10 (02) ◽  
pp. 521-527
Author(s):  
Zhenhui Xu ◽  
Hanlin Chen ◽  
Zhengde Dai
Keyword(s):  
Solitary Wave ◽  
Rogue Wave ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
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.

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
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