All meromorphic solutions of an auxiliary ordinary differential equation and its applications
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In this paper, we first employ the complex method to deritive all meromorphic solutions of an auxiliary ordinary differential equation, and then find all meromorphic exact solutions of the modified ZK equation, modified KdV equation, nonlinear Klein-Gordon equation and modified BBM equation. Our work shows that there exist some classes of rational solutions wr,2(z) and simple periodic solutions ws,1(z) which are new and are not degenerated successively to by the elliptic function solutions.
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All meromorphic solutions for two forms of odd order algebraic differential equations and its applicationsYuan, W.; Wu, Yong Hong; Chen, Q.; Huang, Y. (2014)In this article, we employ the Nevanlinna’s value distribution theory to investigate the existence of meromorphic solutions of algebraic differential equations. We obtain the representations of all meromorphic solutions ...
Yuan, W.; Meng, F.; Lin, J.; Wu, Yong Hong (2016)In this paper, we employ the complex method to obtain all meromorphic solutions of an auxiliary ordinary differential equation at first and then find out all meromorphic exact solutions of the combined KdV-mKdV equation ...
Meromorphic solutions of a class of algebraic differential equations related to Painlevé equation IIIGu, Y.; Aminakbari, N.; Yuan, W.; Wu, Yong Hong (2017)© 2017 University of Houston. In this paper, the complex method is employed to derive mero-morphic solutions to a class of algebraic differential equations related to Painlevé equation III, and then we illustrate our main ...