Bäcklund transformation andN-soliton solutions for a (2+1)-dimensional nonlinear evolution equation in nonlinear water waves

2014 ◽  
Vol 89 (7) ◽  
pp. 075209 ◽  
Author(s):  
Ya Sun ◽  
Bo Tian ◽  
Wen-Rong Sun ◽  
Yan Jiang ◽  
Yun-Po Wang ◽  
...  
Keyword(s):  
Evolution Equation ◽  
Water Waves ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Bäcklund Transformation ◽  
Soliton Solutions ◽  
Backlund Transformation ◽  
Nonlinear Water Waves

scholarly journals Bäcklund Transformation and Exact Solutions to a Generalized (3 + 1)-Dimensional Nonlinear Evolution Equation

2022 ◽  
Vol 2022 ◽  
pp. 1-12
Author(s):  
Yali Shen ◽  
Ying Yang
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Bäcklund Transformation ◽  
Dynamic Properties ◽  
Traveling Wave Solutions ◽  
Mixed Solution ◽  
Backlund Transformation ◽  
Bilinear Method ◽  
Interaction Solutions

In this article, a generalized (3 + 1)-dimensional nonlinear evolution equation (NLEE), which can be obtained by a multivariate polynomial, is investigated. Based on the Hirota bilinear method, the N-soliton solution and bilinear Bäcklund transformation (BBT) with explicit formulas are successfully constructed. By using BBT, two traveling wave solutions and a mixed solution of the generalized (3 + 1)-dimensional NLEE are obtained. Furthermore, the lump and the interaction solutions for the equation are constructed. Finally, the dynamic properties of the lump and the interaction solutions are described graphically.

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.

Fermionic covariant prolongation structure theory for a (2+1)-dimensional super nonlinear evolution equation

2018 ◽  
Vol 15 (07) ◽  
pp. 1850114 ◽  
Author(s):  
Zhaowen Yan ◽  
Chuanzhong Li
Keyword(s):  
Evolution Equation ◽  
Integrable System ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Bäcklund Transformation ◽  
Structure Theory ◽  
Backlund Transformation ◽  
Prolongation Structure ◽  
New Formula

In the framework of the fermionic covariant prolongation structure theory (PST), we investigate the integrability of a new [Formula: see text]-dimensional super nonlinear evolution equation (NEE). The prolongation structure of the super integrable system is presented. Moreover, we derive the Bäcklund transformation of the super integrable system.

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