All meromorphic solutions for two forms of odd order algebraic differential equations and its applications
MetadataShow full item record
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 for two classes of odd order algebraic differential equations with the weak 〈 p , q 〉 and dominant conditions. Moreover, we give the complex method to find all traveling wave exact solutions of corresponding partial differential equations. As an example, we obtain all meromorphic solutions of some generalized Bretherton equations by using our complex method. Our results show that the complex method provides a powerful mathematical tool for solving great many nonlinear partial differential equations in mathematical physics, and using the traveling wave nobody can find other new exact solutions for many nonlinear partial differential equations by any method.
Showing items related by title, author, creator and subject.
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 ...
Yuan, W.; Xiong, W.; Lin, J.; Wu, Yong Hong (2015)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 ...
Yuan, W.; Xiao, B.; Wu, Yong Hong; Qi, J. (2014)In this article, we introduce two recent results with respect to the integrality and exact solutions of the Fisher type equations and their applications. We obtain the sufficient and necessary conditions of integrable and ...