Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 15, Issue 10, Pages 2778-2790Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2009.11.013
Keywords
Nonlinear ordinary differential equation; Riccati equation; Exact solution; Laurent series; Meromorphic solution; Exp-function method; Burgers equation; Korteweg-de Vries equation; Kuramoto-Sivashinsky equation; Kawahara equation
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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. (C) 2009 Elsevier B.V. All rights reserved.
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