Meromorphic solutions of nonlinear partial differential equations and many‐particle completely integrable systems

1979 ◽  
Vol 20 (12) ◽  
pp. 2416-2422 ◽  
Author(s):  
D. V. Chudnovsky
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integrable Systems ◽  
Nonlinear Partial Differential Equations ◽  
Meromorphic Solutions ◽  
Completely Integrable Systems ◽  
Partial Differential ◽  
Completely Integrable

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.

ON MEROMORPHIC SOLUTIONS OF GENERALIZED FERMAT EQUATIONS

2014 ◽  
Vol 25 (01) ◽  
pp. 1450002 ◽  
Author(s):  
BAO QIN LI
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Meromorphic Solutions ◽  
Partial Differential

Meromorphic solutions f, g of the equations fp + gq = 1 in C2 with p, q ≥ 2 being integers are not necessarily constant. We show that they always are, if fz2 and gz1 have the same zeros. An application is also given to characterize meromorphic solutions of related nonlinear partial differential equations.

Sign in / Sign up

Export Citation Format

Share Document