scholarly journals Painlevé Analysis and Abundant Meromorphic Solutions of a Class of Nonlinear Algebraic Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yongyi Gu ◽  
Xiaoxiao Zheng ◽  
Fanning Meng
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Gordon Equation ◽  
Kdv Equation ◽  
Painlevé Analysis ◽  
Complex Method ◽  
Meromorphic Solutions ◽  
Sine Gordon Equation ◽  
Algebraic Differential Equations ◽  
Painleve Analysis

In this paper, a class of nonlinear algebraic differential equations (NADEs) is studied. The Painlevé analysis of the NADEs is considered. Abundant meromorphic solutions of the NADEs are obtained by means of the complex method. Then, meromorphic exact solutions of the Schamel-Korteweg-de Vries (S-KdV) equation and (2+1)-dimensional sine-Gordon equation are derived via the applications of the NADEs.

scholarly journals On the Exact Solutions of Two (3+1)-Dimensional Nonlinear Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Fanning Meng ◽  
Yongyi Gu
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Shallow Water ◽  
Traveling Wave ◽  
Nonlinear Differential Equations ◽  
Complex Method ◽  
Meromorphic Solutions ◽  
Complex Differential Equations ◽  
Bkp Equation

In this article, exact solutions of two (3+1)-dimensional nonlinear differential equations are derived by using the complex method. We change the (3+1)-dimensional B-type Kadomtsev-Petviashvili (BKP) equation and generalized shallow water (gSW) equation into the complex differential equations by applying traveling wave transform and show that meromorphic solutions of these complex differential equations belong to class W, and then, we get exact solutions of these two (3+1)-dimensional equations.

scholarly journals A Note on the Fractional Generalized Higher Order KdV Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Yongyi Gu
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Nonlinear Differential Equations ◽  
Mathematical Physics ◽  
Higher Order ◽  
Complex Method ◽  
Applied Method ◽  
De Vries

We obtain exact solutions to the fractional generalized higher order Korteweg-de Vries (KdV) equation using the complex method. It has showed that the applied method is very useful and is practically well suited for the nonlinear differential equations, those arising in mathematical physics.

Exact solutions and Painlevé analysis of a new (2+1)-dimensional generalized KdV equation

2011 ◽  
Vol 68 (4) ◽  
pp. 445-458 ◽  
Author(s):  
Yi Zhang ◽  
Yang Song ◽  
Li Cheng ◽  
Jian-Ya Ge ◽  
Wei-Wei Wei
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Painlevé Analysis ◽  
Generalized Kdv Equation ◽  
Painleve Analysis

scholarly journals Exact Analytical Solutions of Generalized Fifth-Order KdV Equation by the Extended Complex Method

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mehvish Fazal Ur Rehman ◽  
Yongyi Gu ◽  
Wenjun Yuan
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Analytical Solutions ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Complex Method ◽  
Exact Analytical Solutions ◽  
Extended Complex ◽  
Fifth Order ◽  
Physical Phenomena

The recently introduced technique, namely, the extended complex method, is used to explore exact solutions for the generalized fifth-order KdV equation. Appropriately, the rational, periodic, and elliptic function solutions are obtained by this technique. The 3D graphs explain the different physical phenomena to the exact solutions of this equation. This idea specifies that the extended complex method can acquire exact solutions of several differential equations in engineering. These results reveal that the extended complex method can be directly and easily used to solve further higher-order nonlinear partial differential equations (NLPDEs). All computer simulations are constructed by maple packages.

scholarly journals Bäcklund Transformation and New Exact Solutions of the Sharma-Tasso-Olver Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Lin Jianming ◽  
Ding Jie ◽  
Yuan Wenjun
Keyword(s):  
Exact Solutions ◽  
Bäcklund Transformation ◽  
Analytic Study ◽  
Bäcklund Transformations ◽  
Painlevé Analysis ◽  
Backlund Transformation ◽  
New Exact Solutions ◽  
Backlund Transformations ◽  
Painleve Analysis

The Sharma-Tasso-Olver (STO) equation is investigated. The Painlevé analysis is efficiently used for analytic study of this equation. The Bäcklund transformations and some new exact solutions are formally derived.

Sign in / Sign up

Export Citation Format

Share Document