Rogue waves, breather waves and solitary waves for a (3+1)-dimensional nonlinear evolution equation

2019 ◽  
Vol 97 ◽  
pp. 6-13 ◽  
Author(s):  
Jingjing Xie ◽  
Xiao Yang
Keyword(s):  
Evolution Equation ◽  
Solitary Waves ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Rogue Waves

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.

scholarly journals Degeneration of Solitons for a the (3+1)-dimensional Generalized Nonlinear Evolution Equation for the Shallow Water Waves

2021 ◽  
Author(s):  
longxing li ◽  
Long-Xing Li
Keyword(s):  
Evolution Equation ◽  
Shallow Water ◽  
Water Waves ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Shallow Water Waves ◽  
Hirota Bilinear Form ◽  
Wave Limit

Abstract A the (3+1)-dimensional generalized nonlinear evolution equation for the shallow water waves is investigated with different methods. Based on symbolic computation and Hirota bilinear form, Nsoliton solutions are constructed. In the process of degeneration of N-soliton solutions, T-breathers are derived by taking complexication method. Then rogue waves will emerge during the degeneration of breathers by taking the parameter limit method. Through full degeneration of N-soliton, M-lump solutions are derived based on long wave limit approach. In addition, we also find out that the partial degeneration of N-soliton process can generate the hybrid solutions composed of soliton, breather and lump.

Dynamics of localized waves in a (3+1)-dimensional nonlinear evolution equation

2019 ◽  
Vol 33 (09) ◽  
pp. 1950101 ◽  
Author(s):  
Yunfei Yue ◽  
Yong Chen
Keyword(s):  
Evolution Equation ◽  
Soliton Solution ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Dark Soliton ◽  
Interaction Solutions ◽  
Localized Waves

In this paper, a (3[Formula: see text]+[Formula: see text]1)-dimensional nonlinear evolution equation is studied via the Hirota method. Soliton, lump, breather and rogue wave, as four types of localized waves, are derived. The obtained N-soliton solutions are dark solitons with some constrained parameters. General breathers, line breathers, two-order breathers, interaction solutions between the dark soliton and general breather or line breather are constructed by choosing suitable parameters on the soliton solution. By the long wave limit method on the soliton solution, some new lump and rogue wave solutions are obtained. In particular, dark lumps, interaction solutions between dark soliton and dark lump, two dark lumps are exhibited. In addition, three types of solutions related with rogue waves are also exhibited including line rogue wave, two-order line rogue waves, interaction solutions between dark soliton and dark lump or line rogue wave.

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