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Meromorphic solutions of nonlinear ordinary differential equations

Institution:	1. Department of Mathematics and Center of Nonlinear Equations, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China;2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom;1. Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China;2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China;1. Department of Mathematics and Statistics, Florida International University, Miami, FL 33199, USA;2. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA

Abstract:	Exact solutions of some popular nonlinear ordinary differential equations are analyzed taking their Laurent series into account. Using the Laurent series for solutions of nonlinear ordinary differential equations we discuss the nature of many methods for finding exact solutions. We show that most of these methods are conceptually identical to one another and they allow us to have only the same solutions of nonlinear ordinary differential equations.

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