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 Lump Solutions and Interaction Solutions for the Dimensionally Reduced Nonlinear Evolution Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Baoyong Guo ◽  
Huanhe Dong ◽  
Yong Fang
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Quadratic Functions ◽  
Bilinear Method ◽  
Lump Solutions ◽  
Dynamical Characteristics ◽  
Interaction Solutions ◽  
Physical Quantities ◽  
Hirota Bilinear

In this paper, by means of the Hirota bilinear method, a dimensionally reduced nonlinear evolution equation is investigated. Through its bilinear form, lump solutions are obtained. We construct interaction solutions between lump solutions and one soliton solution by choosing quadratic functions and exponential function. Interaction solutions with the combinations of exponential functions and sine function are also given. Meanwhile, the figures of these solutions are plotted. The dynamical characteristics and properties of obtained solutions are discussed, respectively. The results show that the corresponding physical quantities and properties of nonlinear waves are associated with the values of the parameters.

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.

scholarly journals Lump Solutions, Multi Lump Solutions and More Soliton Solutions of a Novel (2+1)-dimensional Nonlinear Evolution Equation

2021 ◽  
Author(s):  
Hongcai Ma ◽  
Shupan Yue ◽  
Yidan Gao ◽  
Aiping Deng
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Bilinear Method ◽  
Test Function ◽  
Lump Solutions ◽  
Hirota Bilinear ◽  
Test Function Method

Abstract Exact solutions of a new (2+1)-dimensional nonlinear evolution equation are studied. Through the Hirota bilinear method, the test function method and the improved tanh-coth and tah-cot method, with the assisstance of symbolic operations, one can obtain the lump solutions, multi lump solutions and more soliton solutions. Finally, by determining different parameters, we draw the three-dimensional plots and density plots at different times.

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