scholarly journals A Note about the General Meromorphic Solutions of the Fisher Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Jian-ming Qi ◽  
Qiu-hui Chen ◽  
Wei-ling Xiong ◽  
Wen-jun Yuan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Mathematical Physics ◽  
Fisher Equation ◽  
Complex Method ◽  
Mathematical Tool ◽  
Meromorphic Solutions ◽  
Partial Differential ◽  
Powerful Mathematical Tool

We employ the complex method to obtain the general meromorphic solutions of the Fisher equation, which improves the corresponding results obtained by Ablowitz and Zeppetella and other authors (Ablowitz and Zeppetella, 1979; Feng and Li, 2006; Guo and Chen, 1991), andwg,i(z)are new general meromorphic solutions of the Fisher equation forc=±5i/6.Our results show that the complex method provides a powerful mathematical tool for solving great many nonlinear partial differential equations in mathematical physics.

scholarly journals Meromorphic solutions of the (2 + 1)- and the (3 + 1)-dimensional BLMP equations and the (2 + 1)-dimensional KMN equation

2021 ◽  
Vol 54 (1) ◽  
pp. 129-139
Author(s):  
Guoqiang Dang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Complex Plane ◽  
Nonlinear Partial Differential Equations ◽  
Complex Method ◽  
Meromorphic Solutions ◽  
Rational Solutions ◽  
Partial Differential ◽  
Elliptic Solutions

Abstract The complex method is systematic and powerful to build various kinds of exact meromorphic solutions for nonlinear partial differential equations on the complex plane C {\mathbb{C}} . By using the complex method, abundant new exact meromorphic solutions to the ( 2 + 1 ) \left(2+1) -dimensional and the ( 3 + 1 ) \left(3+1) -dimensional Boiti-Leon-Manna-Pempinelli equations and the ( 2 + 1 ) \left(2+1) -dimension Kundu-Mukherjee-Naskar equation are investigated. Abundant new elliptic solutions, rational solutions and exponential solutions have been constructed.

scholarly journals The General Traveling Wave Solutions of the Fisher Equation with Degree Three

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Wenjun Yuan ◽  
Qiuhui Chen ◽  
Jianming Qi ◽  
Yezhou Li
Keyword(s):  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Necessary Condition ◽  
Complex Method ◽  
Mathematical Tool ◽  
Meromorphic Solutions ◽  
Sufficient And Necessary Condition ◽  
Powerful Mathematical Tool

We employ the complex method to research the integrality of the Fisher equations with degree three. We obtain the sufficient and necessary condition of the integrable of the Fisher equations with degree three and the general meromorphic solutions of the integrable Fisher equations with degree three, which improves the corresponding results obtained by Feng and Li (2006), Guo and Chen (1991), and Ağırseven and Öziş (2010). Moreover, allwg,1(z)are new general meromorphic solutions of the Fisher equations with degree three forc=±3/2. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.

scholarly journals Improved General Mapping Deformation Method for Nonlinear Partial Differential Equations in Mathematical Physics

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Khaled A. Gepreel
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Jacobi Elliptic Function ◽  
Deformation Method ◽  
Partial Differential ◽  
General Mapping

We use the improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method to construct some of the generalized Jacobi elliptic solutions for some nonlinear partial differential equations in mathematical physics via the generalized nonlinear Klein-Gordon equation and the classical Boussinesq equations. As a result, some new generalized Jacobi elliptic function-like solutions are obtained by using this method. This method is more powerful to find the exact solutions for nonlinear partial differential equations.

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