All meromorphic solutions of some algebraic differential equations and their applications

In this paper, we employ Nevanlinna's value distribution theory to investigate the existence of meromorphic solutions of some algebraic differential equations. We obtain the representations of all meromorphic solutions of certain algebraic differential equations with constant coefficients and dominant term. Many results are the corollaries of our result, and we will 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 the Kuramoto-Sivashinsky equation 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.